MATH DAY 2012mdashTEAM COMPETITION

An excursion through mathematics and its history

A quick review of the rules History (or trivia) questions alternate with math

questions Math questions are numbered by MQ1 MQ2 etc

History questions by HQ1 HQ2 etc Math answers should be written on the appropriate

sheet of the math answers booklet History questions are multiple choice answered using

the clicker Math questions are worth the number of points shown

on the screen when the runner gets your answer sheet That equals the number of minutes left to answer the question

Have one team member control the clicker another one the math answers booklet

Rules--Continued

All historytrivia questions are worth 1 point

The team with the highest math score is considered first Next comes the team with the highest history score from a school different from the school of the winning math team Finally the team with the highest overall score from the remaining schools

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called20 seconds

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

A quick review of the rules History (or trivia) questions alternate with math

questions Math questions are numbered by MQ1 MQ2 etc

History questions by HQ1 HQ2 etc Math answers should be written on the appropriate

sheet of the math answers booklet History questions are multiple choice answered using

the clicker Math questions are worth the number of points shown

on the screen when the runner gets your answer sheet That equals the number of minutes left to answer the question

Have one team member control the clicker another one the math answers booklet

Rules--Continued

All historytrivia questions are worth 1 point

The team with the highest math score is considered first Next comes the team with the highest history score from a school different from the school of the winning math team Finally the team with the highest overall score from the remaining schools

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called20 seconds

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Rules--Continued

All historytrivia questions are worth 1 point

The team with the highest math score is considered first Next comes the team with the highest history score from a school different from the school of the winning math team Finally the team with the highest overall score from the remaining schools

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called20 seconds

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called20 seconds

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

called20 seconds

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ0-Warm Up no points

Non Euclidean Geometry is so called because

A It was invented by Non EuclidB It negates Euclidrsquos parallel

postulateC It negates all of Euclidrsquos postulatesD Euclid did not care for itE Nobody really knows why it is so

calledTimes Up

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the points system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 5

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 4

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 3

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 2

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Demonstrating the point system For math questions there will be a

number in the lower right corner It will change every minute Here I am illustrating with numbers changing every 10 seconds Try to imagine 10 seconds is a minute The first number tells you the maximum number of points you can get for the question Assume a question is on the screen 1

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

THE CHALLENGE BEGINS

VERY IMPORTANTPut away all electronic devices including calculators Mechanical devices invented more than a hundred years ago are OK

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

20 seconds

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ1 Babylonians

One of the oldest of all known civilizations is that of the Babylonians with capital in Babylon Where was the city of Babylon located

A In EgyptB In GreeceC In IraqD In TurkeyE In Florida

Times Up

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

The Babylonians

The name Babylonians is given to the people living in the ancient Mesopotamia the region between the rivers Tigris and Euphrates modern day Iraq They wrote on clay tablets like the one in the picture The civilization lasted a millennium and a half from about 2000 BCE to 500 BCE

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

3

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

2

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ1-Babylonian TablesA Babylonian tablet has a table listing n3

+n2 for n = 1 to 30 Here are the first 10 entries of such a table

Tables as these seem to have been used to solve cubic equations Solve (using the table or otherwise) for an integer solution

031362 23 xx

Hint Set x = 2n

1

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

20 seconds

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Times Up

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ2 Papyrus Writing

The Rhind or Ahmes papyrus dated to 1650 BCE is one of the oldest remaining mathematical documents Papyrus is a paper like material made from

A Palm leaves

B Cotton

C The stems of a water plant

D The leaves of a desert lily

E Apple peels

Papyrus is made from the stems of the papyrus plant a reed like plant growing on the shores of the Nile

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 3

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 2

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share 1

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ2 Solve like an Egyptian

This problem appears in the Rhind papyrusDivide 100 loaves among 5 men in such a way that the shares received shall be in arithmetic progression and that one seventh of the sum of the largest 3 shares shall be equal to the sum of the smallest two

All shares but the third (middle) one are fractions What is the middle share

Answer 20

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch out20 seconds

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ3 Pythagoreans Hippasus the Pythagorean is said to have

drowned at sea or suffered some other punishment for revealing

A That there was an infinity of numbersB That some numbers could not be

expressed as a quotient of integersC That every number could be expressed as

a product of primesD That some perfect squares are sums of

perfect squaresE That numbers will get you if you donrsquot

watch outTimes Up

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

More on Pythagoras and his friends

The Pythagoreans were a secret society flourishing ca 600-400 BC They called themselves followers of Pythagoras of Samos who may or may not have existed The most important achievement of the Pythagoreans was the discovery of irrational numbers specifically The hypotenuse of a righttriangle of legs of length 1 is incommensurable with the legs Or

as we say now the square root of 2 is irrational cannot be expressed as a ratio of two integers

The Pythagoreans loved numbers they adored numbers they said ldquoEverything is numberrdquo A property that amazed them was the existence of what they called amicable or friendly numbers A pair of numbers m n is an amicable pair if each is the sum of the proper divisors of the other one

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

Pythagoras and his friends

Their only example was the pair 220 284

The proper divisors of 220 are 1 2 4 5 10 11 20 22 44 55 110

1+2+4+5+10+11+20+22+44+55+110 = 284

The proper divisors of 284 are 1 2 4 71 142

1+2+4+71+142 = 220

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

4

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

3

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

2

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ3 Looking for FriendsIt is known that 1184 is a member of an amicable pair

It is feeling lonely Find its friend

1

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

The answer is 1210 To find the divisors of 1184 we can

start seeing that it is even see how many powers of 2 divide it 11842 = 592 5922 = 296 2962 = 148 1482 = 74 742 = 37 and 37 is prime That is 1184 = 2537 The divisors are all of the form 2p and 2p

37 0 le p le 5

1+2+4+8+16+32+37+74+148+296+592 = 1210

5923716296378148374

743723737132168421

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ4 The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

20 seconds

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ The invention of nothingThe number 0 in its modern form and

the concept of a negative number first appears in

A IndiaB GreeceC RomeD EgyptE China

Timersquos Up

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

3

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

2

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

1

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ4 Brahmaguptarsquos legacy

A quadrilateral of sides of lenghts 4 5 7 and 10 is inscribed in a circle The radius of the circle can be expressed in the form where m n s are positive integers the greatest common divisor of m and n is 1 and s is square free Determine m + n + s

n

smR

The answer is 78

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

20 seconds

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

Timersquos Up

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ5 Fibonaccirsquos rabbits

The title of the book in which Fibonacci has the famous rabbit problem solved by the famous Fibonacci sequence is

A The book of numbersB The book of the golden meanC The book of calculationsD The book of sumsE Peter Rabbit and family

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

4

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

3

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

2

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

1

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The Fibonacci sequence is an example of a sequence defined recursively Here is another example The sequence of numbers

a0 a1 a2 a3 a4

satisfies if n ge 2 If

a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

The answer is 7

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ5 Recurrence

The sequence of numbers a0 a1 a2 a3 a4 satisfies

if n ge 2 If a0 = 3 and a5 = 307 what is a1

21 65 nnn aaa

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

20 seconds

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

D To discuss the logarithmic spiral and its applications

E To warn people about the danger of breeding rabbits

Timersquos Up

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ6 Talking of Fibonacci

Leonardo Pisano(1170-1250)

One of the main purposes of Fibonaccirsquos book was

A To discuss sequences and show how they can be used

B To introduce the Arabic numerals to Europe

C To introduce new techniques for solving equations

Liber Abaci begins with``The nine Indian figures are9 8 7 6 5 4 3 2 1With these nine figures and with sign 0 which the Arabs call zephir any number whatsoeveris written as is demonstrated belowrsquorsquo

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

20 seconds

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

Times Up

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ7 Donkeys Crossing The fifth proposition in the first volume of Euclidrsquos elements was known as the ``pons asinorumrsquorsquo ``bridge of assesrsquorsquo It states

A If in a triangle two angles equal each other then the triangle is isosceles

B In an isosceles triangle the base angles are equal

C In any triangle the sum of any two sides is greater then the remaining side

D In any triangle the sum of the three interior angles of the triangle equals two right angles

E In any triangle the side opposite the greater angle is greater

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Find a + b Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

3

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

2

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

1

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ6 Circles Let R be the radius of the circumscribed

r the radius of the inscribed circle of a triangle of sides 21 20 13 The ratio Rr can be expressed as a ratio of two positive integers a b with no common divisors other than 1 Rr = ab gcd(ab)=1 What is a+b Possible hint 21 = 5+16

The answer is 93

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

20 seconds

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ8 The Word Became NumberThe inventor of logarithms wasA An Italian priest

B A Greek mathematician

C A Scottish nobleman

D A German philosopher

E A Chinese mathematician

Times Up

John Napier(1550-1617)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

2

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625

1

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ7 Logarithms

With log being logarithm in base 10 compute

log 2 + log 4 + log 8 + log 25 + log 625 =

log (2times4times8times25times625) = log(106) = 6

The answer is 6

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

20 seconds

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ9The Renaissance

Rafael Bombelli was one of the leading mathematicians of the 16th century He was born in the city whose university founded 1088 may be the oldest in the world That city is

A RomeB VeniceC PisaD FlorenceE Bologna

Timersquos Up

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

5

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

4

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

3

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

2

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

1

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

TIMErsquos UP

>

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

MQ8 From Bombellirsquos AlgebraA square is inscribed in triangle ABC with one side on BCIf |AB| = 13 |BC| = 14 |CA| = 15 the length of the side of the square has the form ab where a b are positive integers with no common divisor other than 1 Find a + b

The answer is 97

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen Hawking20 seconds

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ10 Mathematical AdvancesWho said ldquoStandard mathematics has recently been

rendered obsolete by the discovery that for years we have been writing the numeral five backward This has led to reevaluation of counting as a method of getting from one to ten Students are taught advanced concepts of Boolean algebra and formerly unsolvable equations are dealt with by threats of reprisalsrdquo

A Woody Allen

B Jon Stewart

C Stephen Colbert

D Lord Bertrand Russell

E Stephen HawkingTimes Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

20 seconds

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ11 Back to the PythagoreansWhich of the following was

NOT a rule the Pythagoreans had to follow

A Donrsquot eat beans

B Never stir the fire with a knife

C Touch the earth when it thunders

D Spit on your nail pairings and hair trimmings

E No women are allowed at the meetings

Times Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna Austria20

seconds

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ12 Euler

Leonhard Euler (1707-1783) was the greatest mathematician of the 18th century and one of the greatest of all times He was born in

A Basel SwitzerlandB Berlin GermanyC Bonn GermanyD Salzburg AustriaE Vienna AustriaTimersquos Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

10 seconds

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

Times Up

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ13 Etymologies

The word algebra isA Of Greek originB Of Arabic originC Of Indian originD Of Latin originE Of Italian origin

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether 10 seconds

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ14 Women in mathematicsShe was one of the very important

mathematicians of the 20th century making essential contributions to both abstract algebra and physics She was recently the subject of a long article in the New York Times Her name is

A Frances LangfordB Matilda NeubergerC Lise MeitnerD Anne DubreilE Emmy Noether Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre 10 seconds

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ15 A French nobleman

The Marquis of LrsquoHocircpital (1661-1704) was the author of the very first Calculus textbook His famous rule appears in it But it seems the book was really written by

A Isaak NewtonB Johan BernoulliC Gottfried LeibnizD Isaak BarrowE Abraham DeMoivre Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime 10 seconds

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime Timersquos Up

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)

HQ16 Conjectures

The Goldbach conjecture statesA Every even integer greater than 4 is a

sum of two primesB There exists an infinity of primes p such

that p+2 is also primeC There exists an infinity of primes of the

form 5k+7 where k is a positive integerD If 2p ndash 1 is prime then p is primeE An infinite number of Fibonacci numbers

are prime

• MATH DAY 2012mdashTeam Competition
• A quick review of the rules
• Rules--Continued
• HQ0-Warm Up no points
• HQ0-Warm Up no points (2)
• HQ0-Warm Up no points (3)
• HQ0-Warm Up no points (4)
• Demonstrating the points system
• Demonstrating the point system
• Demonstrating the point system (2)
• Demonstrating the point system (3)
• Demonstrating the point system (4)
• Demonstrating the point system (5)
• Slide 14
• Slide 15
• HQ1 Babylonians
• HQ1 Babylonians (2)
• HQ1 Babylonians (3)
• HQ1 Babylonians (4)
• The Babylonians
• MQ1-Babylonian Tables
• MQ1-Babylonian Tables (2)
• MQ1-Babylonian Tables (3)
• MQ1-Babylonian Tables (4)
• Slide 25
• Slide 26
• HQ2 Papyrus Writing
• HQ2 Papyrus Writing (2)
• HQ2 Papyrus Writing (3)
• HQ2 Papyrus Writing (4)
• MQ2 Solve like an Egyptian
• MQ2 Solve like an Egyptian (2)
• MQ2 Solve like an Egyptian (3)
• MQ2 Solve like an Egyptian (4)
• Slide 35
• MQ2 Solve like an Egyptian (5)
• HQ3 Pythagoreans
• HQ3 Pythagoreans (2)
• HQ3 Pythagoreans (3)
• HQ3 Pythagoreans (4)
• More on Pythagoras and his friends
• Pythagoras and his friends
• MQ3 Looking for Friends
• MQ3 Looking for Friends (2)
• MQ3 Looking for Friends (3)
• MQ3 Looking for Friends (4)
• MQ3 Looking for Friends (5)
• Slide 48
• The answer is 1210
• HQ4 The invention of nothing
• HQ4 The invention of nothing (2)
• HQ The invention of nothing
• HQ The invention of nothing (2)
• MQ4 Brahmaguptarsquos legacy
• MQ4 Brahmaguptarsquos legacy (2)
• MQ4 Brahmaguptarsquos legacy (3)
• MQ4 Brahmaguptarsquos legacy (4)
• Slide 58
• MQ4 Brahmaguptarsquos legacy (5)
• HQ5 Fibonaccirsquos rabbits
• HQ5 Fibonaccirsquos rabbits (2)
• HQ5 Fibonaccirsquos rabbits (3)
• HQ5 Fibonaccirsquos rabbits (4)
• MQ5 Recurrence
• MQ5 Recurrence (2)
• MQ5 Recurrence (3)
• MQ5 Recurrence (4)
• MQ5 Recurrence (5)
• Slide 69
• MQ5 Recurrence (6)
• MQ5 Recurrence (7)
• HQ6 Talking of Fibonacci
• HQ6 Talking of Fibonacci (2)
• HQ6 Talking of Fibonacci (3)
• HQ6 Talking of Fibonacci (4)
• HQ7 Donkeys Crossing
• HQ7 Donkeys Crossing (2)
• HQ7 Donkeys Crossing (3)
• HQ7 Donkeys Crossing (4)
• MQ6 Circles
• MQ6 Circles (2)
• MQ6 Circles (3)
• MQ6 Circles (4)
• Slide 84
• MQ6 Circles (5)
• HQ8 The Word Became Number
• HQ8 The Word Became Number (2)
• HQ8 The Word Became Number (3)
• HQ8 The Word Became Number (4)
• MQ7 Logarithms
• MQ7 Logarithms (2)
• MQ7 Logarithms (3)
• Slide 93
• MQ7 Logarithms (4)
• HQ9The Renaissance
• HQ9The Renaissance (2)
• HQ9The Renaissance (3)
• HQ9The Renaissance (4)
• MQ8 From Bombellirsquos Algebra
• MQ8 From Bombellirsquos Algebra (2)
• MQ8 From Bombellirsquos Algebra (3)
• MQ8 From Bombellirsquos Algebra (4)
• MQ8 From Bombellirsquos Algebra (5)
• MQ8 From Bombellirsquos Algebra (6)
• Slide 105
• MQ8 From Bombellirsquos Algebra (7)
• HQ10 Mathematical Advances
• HQ10 Mathematical Advances (2)
• HQ10 Mathematical Advances (3)
• HQ10 Mathematical Advances (4)
• HQ11 Back to the Pythagoreans
• HQ11 Back to the Pythagoreans (2)
• HQ11 Back to the Pythagoreans (3)
• HQ11 Back to the Pythagoreans (4)
• HQ12 Euler
• HQ12 Euler (2)
• HQ12 Euler (3)
• HQ12 Euler (4)
• HQ13 Etymologies
• HQ13 Etymologies (2)
• HQ13 Etymologies (3)
• HQ13 Etymologies (4)
• HQ14 Women in mathematics
• HQ14 Women in mathematics (2)
• HQ14 Women in mathematics (3)
• HQ14 Women in mathematics (4)
• HQ15 A French nobleman
• HQ15 A French nobleman (2)
• HQ15 A French nobleman (3)
• HQ15 A French nobleman (4)
• HQ16 Conjectures
• HQ16 Conjectures (2)
• HQ16 Conjectures (3)
• HQ16 Conjectures (4)