The History of Mathematics

http://www-groups.dcs.st-and.ac.uk/~history/BiogIndex.html

http://www.math.wichita.edu/~richardson/timeline.html

http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html

x2 + 10 x = 39

x2 + 10 x + 4·25/4 = 39+25

(x+5)2 = 64

x + 5 = 8

x = 3

al-Khwarizmi Iraq (ca. 780-850)

Completing a SquareSolving a Quadratic Equation

•In Konigsberg, Germany, a river ran through the city such that in its centre was an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people of the city could get from one part to another.

•The people wondered whether or not one could walk around the city in a way that would involve crossing each bridge exactly once

The Bridges of KonigsbergTopologyLeonhard Euler

Switzerland 1707 - 1783

The city

Theorem: There are infinitely many prime numbers. Proof:Suppose the opposite, that is, that there are a finite number of prime numbers. Call them p1, p2, p3, p4,....,pn. Now consider the number •(p1*p2*p3*...*pn)+1

•Every prime number, when divided into this number, leaves a remainder of one. So this number has no prime factors (remember, by assumption, it's not prime itself).

•This is a contradiction. Thus there must, in fact, be infinitely many primes.

Infinite Prime NumbersEuclid

Greece 325 – 265BC

The Search for PiPerson/People Year Value

Babylonians ~2000 B.C. 3 1/8

Egyptians ~2000 B.C. (16/9)^2= 3.1605

Archimedes - Italy ~300 B.C.proves 3 10/71<Pi<3 1/7

uses 211875/67441=3.14163

Ptolemy - Greece ~200 A.D. 377/120=3.14166...

Tsu Chung-Chi - China

~500 A.D. proves 3.1415926<Pi<3.1415929

Aryabhatta - Indian ~500 3.1416

Fibonacci - Italy 1220 3.141818

Ludolph van Ceulen - German

1596 Calculates Pi to 35 decimal places

Machin - England 1706 100 decimal places

CDC 6600 1967 500,000 decimal places

•François Viète (1540-1603) France - determined that:

•John Wallis (1616-1703) English - showed that:

•While Euler (1707-1783) Switzerland derived his famous formula:

•Today Pi is known to more than 10 billion decimal places.

The Search for Pi

Ancient Babylonia

The Sumerians had developed an abstract form of writing based on cuneiform (i.e. wedge-shaped) symbols. Their symbols were written on wet clay

tablets which were baked in the hot sun and many thousands of these tablets have survived to this day. It was the use of a stylus on a clay medium that led to the use of cuneiform symbols since curved lines could not be drawn. The later Babylonians adopted the same style of cuneiform writing on clay tablets.

The Babylonians had an advanced number system, in some ways more advanced than our present

systems. It was a positional system with a base of 60 rather than the system with base 10 in widespread

use today.

Laura T

The Four Colour Conjecture was first stated just over 150 years ago, and finally

proved conclusively in 1976. It is an outstanding example of

how old ideas combine with new discoveries and techniques in different fields of

mathematics to provide new approaches to a problem. It is also an example of how an apparently simple

problem was thought to be 'solved' but then became more

complex, and it is the first spectacular example where

a computer was involved in proving a

mathematical theorem.

The Four Colour Theorem

The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting has survived for 4000 years. To write 5h 25' 30", i.e. 5 hours, 25 minutes, 30 seconds, is just to write the sexagesimal fraction, 5 25/60 30/3600. We adopt the notation 5; 25, 30 for this sexagesimal number, for more details regarding this notation see our article on Babylonian numerals. As a base 10 fraction the sexagesimal number 5; 25, 30 is 5 4/10 2/100 5/1000 which is written as 5.425 in decimal notation.

Laura T

Ancient Babylonia

Perhaps the most amazing aspect of the Babylonian's calculating skills was their construction of tables to aid calculation. Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 BC. They give squares of the numbers up to 59 and cubes of the numbers up to 32. The table gives 82 = 1,4 which stands for 82 = 1, 4 = 1 x 60 + 4 x 1 = 64 and so on up to 592 = 58, 1 = 58 x 60 +1 x 1 = 3481).

The Babylonians used the formula ab = [(a + b)2 - a2 - b2]/2 to make multiplication easier. Even better is their formula ab = [(a + b)2 - (a - b)2]/4 which shows that a table of squares is all that is necessary to multiply numbers, simply taking the difference of the two squares that were looked up in the table then taking a quarter of the answer.

Laura T

Ancient Babylonia

Egyptian numerals

        

or

Value 1 10 100 1,000 10,000

100,000

1 million, or

infinity

Hieroglyph

Description

Single stroke

Heel bone

Coil of rope

Water lily

(also called Lotus)

Finger Tadpole

or Frog

Man with both

hands raised

   

   

   

  

          

The following hieroglyphs were used to denote powers of ten:

Laura T

Multiples of these values were expressed by repeating the symbol as many times as needed. For instance, a stone carving from Karnak shows the number 4622 as

Chinese Mathematics

Jeremy

Chinese mathematics has developed greatly since at least 100 BC. Although the Chinese refer back to their ancient texts, many of which were written on strips of bamboo, they are constantly coming up with ways of working out problems. One of the earliest Chinese mathematicians was a man named Luoxia Hong (130BC – 30BC). He designed a new calendar for the Emperor, which featured 12 months, based on a cycle of 12 years. This inspired many people to design calendars and the one we have today.

The Chinese also came up with a rule called the Gougu Rule. This is the Chinese version of Pythagoras. Liu Hui (220AD – 280AD) tried to find pi to the nearest number. He eventually got to 3.14159, which in those days was thought to be an incredible achievement.

The Moscow Papyrus is located in a museum hence the name. The papyrus was copied by a scribe and was brought to Russia. The papyrus contains 25 maths problems involving simple “equations” and solutions. The problems are not in modern form. The problem that has generated the most interest is the volume of a truncated pyramid (a square based pyramid with the top portion removed). The Egyptians discovered the formula for this even though it was very hard to derive.

The Moscow Papyrus is 15 feet long and about 3 inches wide.

The Actual author of the equation is unknown. But this is what he/she discovered:

Alannah

Johannes Widman was a German mathematician who is best remembered for an early arithmetic book which contains the first appearance of + and – (both adding and subtracting, and positive and negative) signs in 1498.

His book was better than anybody else's because he had more and a wider range of examples.

The book remained in print until 1526.(28 years after it was first published.)

Alannah

Moscow Papyrus: ArithmeticAs it name may suggest, the Moscow papyrus is located in the Museum of Fine Arts in Moscow.

In around 1850BC, the papyrus was copied by an anonymous scribe and was bought to Russia in the 19th Century.

It contains 25 problems containing simple equations and solutions.

However, the equations are not in modern form.

The problem that generates the most interest is the calculation of the volume of a truncated pyramid (a square based pyramid with the top cut off)

The Egyptians seemed to know this difficult formula.

V= (1/3)(a² + ab + b²)(h) Alex

Johannes Widman (1462 – 1498)

Widman is best known for a book on arithmetic which he wrote (in German) in 1489AD.

This contains the first appearance of + and – signs. This was better than those that had come before it with a wider range of examples.

The book continued to be published until 1526AD. Then, Adam Ries – amongst others – produced superior books.

Alex

Chu Shih-chieh (Zhu Shijie)

Zhu Shijie was one of the greatest Chinese mathematicians. He lived during the Yuan Dynasty.

Yang worked on magic squares and binomial theorem, and is best known for his contribution of presenting 'Yang Hui's Triangle'. This triangle was the same as Pascal's Triangle, discovered independently by Yang and his predecessor Jia Xian .Yang was also a friend to the other famous mathematician Qin Jiushao.

An early form of Pascal’s triangle

Calum

Magic squaresIn mathematics, a magic square of

order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

A normal magic square contains the integers from 1 to n².

All non trivial magic squares exist for n≥3.

An example of a magic square

The equation

Calum

Johannes Widmann

Johannes Widmann (born c. 1460 in Eger; died after 1498 in Leipzig) was a German mathematician who was the first to use the addition (+) and the subtraction (-) signs. Widmann attended the University of Leipzig in the 1480s, and published Behende und hubsche Rechenung auff allen Kauffmanschafft, his work making use of the signs, in Leipzig in 1489.

+Calum

-

AristarchusAristarchus of Samos was a Greek mathematician and astronomer.

He was born in about 310BC and died at around 230BC.

He is the first person to suggest a universe with the Sun at the centre instead of the Earth.

He tried to work out the sizes of the Sun and the Moon and how far away they are. He worked out that the Sun was 20 times further away than the moon and 20 times bigger. Both these estimates were too small but the reasoning behind it was right.

Charis

Blaise Pascal (1623-1662)Pascal was a French mathematician and physicist.His father was a tax official and Pascal made a calculating machine

that did addition and subtraction to make his work easier.

He wrote about Pascal's triangle. Each number is the sum of the two above it.

There are lots of different patterns in the triangle. Some are shown on the diagram.

Pascal also worked with Fermat on the theory of probability, and he wrote about projective geometry when he was only 16.

Charis

Pythagoras and the Mathematikoi - Pythagoras was the leader of a Society which consisted mainly of followers called the mathematikoi.

- The mathematikoi owned nothing personal and were vegetarians.

- Any mathematical discoveries they made the credit was given to Pythagoras.

- Everything we know about Pythagoras and the mathematikoi was only recorded properly 100 years later as they apparently wrote none of their information down.

David

Trigonometry of Hipparchus

-Hipparchus was a Greek mathematician who invented one of the first trigonometry

tables which he needed to compute the orbits of the Sun and Moon.

-The table on the right represents the Chord function. The chord of an angle is the length

between two points on a unit circle separated by that angle.

-If one the angles is zero it can be easily related to the sine function. And the used

in the half angle formula:

David

JAPANESE MATHEMATICS= 6 0 = 1 6

http://en.wikipedia.org/wiki/Japanese_numerals

The system of Japanese numerals is the system of numbernames used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000. Like in Chinese numerals, there exists in Japanese a separate set of kanji for numerals called daiji (大字 ) used in legal and financial documents to prevent unscrupulous individualsfrom adding a stroke or two, turning a one into a two or a three. The formal numbers are identical to the Chinese formalnumbers except for minor stroke variations

George

John Napier ( 1550-1617)• Napier was a Scottish mathematician

who studied math like a hobby as he never had time to spend on calculations between working on theology.

• He is best known, along with Joost Burgi, for his invention of logarithms

• He is also famous for the invention of two theories:

1. Napier’s analogy (used in solving spherical triangles)

2. And Napier’s bones. (used for mechanically multiplying, dividing, taking square roots and cube roots

Hannah

Pierre de Fermat (1601- 1665)• Fermat was a French mathematician

who is best known for his work on number and theory

• One of his last theorem’s was proven by Andrew Wiles in 1994.

• Whilst in Bordeaux, Fermat produced work on maxima and minima, which was important. His methods of doing this were similar to ours , however as he has not a professional mathematician his work was very awkward.

• Fermat’s last theorem was that if you had the equation : xn + yn = zn

n in this equation can be no more that two.

When n is more than two the equation does not work

Hannah

HipparchusHipparchus is most known for Trigonometry. He did not discover this on his own however. Menelaus and Ptolomy, helped with this.

“Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." some historians say. Some even go as far as to say that he invented trigonometry.

Not much is known about the life of Hipparchus. But it is believed that he was born at Nicaea in Bithynia, and lived from 190 BC to 120 BC

Issy

AlgebraAlgebra is a branch of mathematics concerning the study of structure, relation, and quantity. Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics.

Elementary algebra is provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements.

The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax² + bx = c) equations, as well as indeterminate equations such as x² + y² = z², whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations

Issy

The Roman Abacus• The Roman Abacus was devised by Roman traders adapting ideas that had been picked up in Egypt.

•The Abacus is made up of grooves in a slate tile with marbles that run in them.

•The Abacus was originally made in Babylon using stones and ditched made in the dry soil in 2700 BC.

•The Abacus was originally made in Babylon using stones and ditched made in the dry soil in 2700 BC.

•Each Abacus used a different scale depending on the user. Traders often used ones with fractions up to 1/12.

•This would mean that they could subtract quite accurately eg. To subtract 1/3 you would take a bead from the 1/4 column and one from the 1/12 column.

John-Jack

Buffon’s needle problem

• Georges-Louis Leclerc, Comte de Buffon lived from in September 7, 1707 to April 16, 178.• He had many different careers, as a naturalist, mathematician, biologist, cosmologist and author.• The Lycée Buffon in Paris is named after him.• The problem he is famous for is:

Suppose we have a floor made of parallel strips of wood, each the same

width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Or in more mathematical terms …

Given a needle of length l dropped on a plane ruled with parallel lines t units apart, what is the probability that the needle will cross a line?

• For n needles dropped with h of the needles crossing lines, the probability is:

This is useful because it can be rearranged to get an estimate for pi

Laura W

The Egyptians had a writing system based on hieroglyphs from around 3000 BC. Hieroglyphs are little pictures representing words. It is easy to see how they would denote the word "bird" by a little picture of a bird but clearly without further development this system of writing cannot represent many words. The way round this problem adopted by the ancient Egyptians was to use the spoken sounds of words. For example, to illustrate the idea with an English sentence, we can see how "I hear a barking dog" might be represented by: "an eye", "an ear", "bark of tree" + "head with crown", "a dog". Of course the same symbols might mean something different in a different context, so "an eye" might mean "see" while "an ear" might signify "sound". The Egyptians had a bases 10 system of hieroglyphs for numerals. By this we mean that they has separate symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million.

The Egyptians had a writing system based on hieroglyphs from around 3000 BC. Hieroglyphs are little pictures representing words. It is easy to see how they would denote the word "bird" by a little picture of a bird but clearly without further development this system of writing cannot represent many words. The way round this problem adopted by the ancient Egyptians was to use the spoken sounds of words. For example, to illustrate the idea with an English sentence, we can see how "I hear a barking dog" might be represented by: "an eye", "an ear", "bark of tree" + "head with crown", "a dog". Of course the same symbols might mean something different in a different context, so "an eye" might mean "see" while "an ear" might signify "sound". The Egyptians had a bases 10 system of hieroglyphs for numerals. By this we mean that they has separate symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million.

Kyle

The Addition & Minus SignsThe plus and minus signs are symbols representing positive and negative, the meaning of them has been around since the Egyptian times, but the actual symbols + and – were first published by Johannes Widmann.

Minus

-Addition

A Jewish tradition that dated from at least from the 19th century was to write plus using a symbol like an inverted T. This practice was then adopted into Israeli schools (this practice goes back to at least the 1940s) and is still commonplace today in some elementary schools (including secular schools) while fewer secondary schools. It is also used occasionally in books by religious authors, but most books for adults use the international symbol "+". The usual explanation for the origins of this practice is that it avoided the writing of a symbol "+" that looked like a Christian cross. Unicode has this symbol at position U+FB29 "Hebrew letter alternative plus sign"

Jewish Addition

Symbol

Kyle

CHAOTIC BEHAVIOR In mathematics, chaos theory describes the behaviour of certain dynamical systems – that is, systems whose states evolve with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behaviours of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behaviour is known as deterministic chaos, or simply chaos.Chaotic behaviour is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.

Kyle

Hieroglyphic numerals in Egypt

Hieroglyphs were introduced for numbers in 3000BCE. Their number system was based on units of 10. They used simple grouping to make different numbers.The Egyptians used different images for their hieroglyphs.

Horus was Egyptian God who fought the forces of darkness (in the form of a boar - a pig) and won. His eye is a symbol for Egyptian Unit Fractions.

Each part of the eye is a part of the whole. All the parts of

eye, however, don't add up to the whole. This, some

Egyptologists think, is the sign that the knowledge can never be total, and that one part of the knowledge is not

possible to describe or measure.

                                                                                                                                          

                                

Nina

Pythagoras of Samos• Pythagoras was an ancient Greek mathematician. Pythagoras was born about

569 BC in Samos, Ionia and died about 475 BC.

• Pythagoras invented Pythagoras's theorem which is the idea that in a right angled triangle the two shorter sides squared and added equals the longest side (the hypotenuse) squared.

• It was thought that the Babylonians 1200 years earlier knew this before but Pythagoras was the one to prove it. It is said that this is the oldest numbertheory document in existence. This theorem works for every right

angled triangle

Nina

Algebra• While the word "algebra" comes from Arabic word (al-

jabr)its origins are from the ancient Babylonians. With this system they were able to discover unknown values for a class of problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations.

• The geometric work of the Greeks, typified in the Elements, provided the framework for finding the formulae beyond the solution of particular problems into more general systems of stating and solving equations.

• The Greek mathematicians Hero of Alexandria and Diophantus ("the father of algebra") made algebra into a much higher level. People argye that al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.

Jack G

Algebra• Later, the Indian mathematicians developed

algebraic methods to a high degree of sophistication. Al-Khwarizmi produced the "reduction" and "balancing" (the transposition of subtracted terms),He gave an explanation of solving quadratic equations supported by geometric proofs.

• The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quadratic, quintic and higher-order polynomial equations using numerical methods.

• Gottfried Leibniz discovered the solution to simultaneous equations

Jack G

Napier’s Bones

• Napier’s bones are basically a big multiplication square.

• It was used before calculators for multiplication of !HUGE! Numbers.

• To do a sum using them you arrange the bones in the order of the number to multiply like in the example: the sum is 46785399*7.

• Then, starting from the left, you just add all the numbers in the row, carrying the tens.

http://en.wikipedia.org/wiki/Napier%27s_bones

Paul

Ahmes was the Egyptian scribe who wrote the Rhind Papyrus - one of the oldest known mathematical documents.

Ahmes

Nicole

Born: about 1680 BC in EgyptDied: about 1620 BC in Egypt

• The Rhind Papyrus, which came to the British Museum in 1863, is sometimes called the 'Ahmes papyrus' in honour of Ahmes. Nothing is known of Ahmes other than his own comments in the papyrus.

• Ahmes claims not to be the author of the work, being, he claims, only a

scribe. He says that the material comes from an earlier work of about

2000 BC. • The papyrus is our main source of

information on Egyptian mathematics.

Nicole

Hieroglyphic Numerals

1 10 100 1000 10000

100000 1million or Infinity

Single stroke

Heel bone

Coil of rope

Water Lily

Finger

Tadpole or frog

Man with both hands raised

Hieroglyphics were used by the Egyptians in around 3000BC. These symbols below are what they would use as numbers. Although they only have to write one symbol for one million and we have to do seven, there is a fault. To write one million take one they would have to write 54 symbols.

 

= 999999

Michael

Xenocrates of ChalcedonXenorcrates was a Greek philosopher, mathematician and leader of the platonic army from 339BC to 314BC. Xenocrates is known to have written a book On Numbers, and a Theory of Numbers, besides books on geometry. Plutarch writes that Xenocrates once attempted to find the total number of syllables

Birth: 396BC, Chalcedon

Died: 314BC, Athens

Interests: logic, physics, metaphysics, epistemology, mathematics, ethics.

Ideas: developed the philosophy of Plato.

that could be made from the letters of the alphabet. According to Plutarch, Xenocrates result was 1,002,000,000,000. This possibly represents the first instance that a combinatorial problem involving permutations was attempted. Xenocrates also supported the idea of indivisible lines (and magnitudes) in order to counter Zeno's paradoxes.

Michael

Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi

Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab mathematician who was active in Damascus and Baghdad. He wrote the earliest surviving book on the positional use of the Arabic numerals, around 952. It is especially notable for its treatment of decimal fractions, and that it showed how to carry out calculations without deletions.While the Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggrenn notes that he was mistaken, as decimal fractions were first used five centuries before him by al-Uqlidisi as early as the 10th century.

Michael

Zhu Shijie of ChinaOllie

Zhu Shijie was born in the 13th century near Beijing. Two of his mathematical works have survived; “Introduction to Computational Studies” and “Jade Mirror of Four Unknowns”.This book brought Chinese algebra to its highest level and it is his most important work.He makes use of the Pascal Triangle centuries before Blaise Pascal brought it to common knowledge.

• Francesco Pellos, from Nice, is the earliest example of the use of the decimal point

• He wrote an arithmetic book, called Compendio de lo Abaco, in 1492.

• In this book he makes use of a dot to denote the division of a number by a power of ten. This has evolved to what we now call a decimal point.

Francesco Pellos 1450 – 1500 AD

Thales (620-547BC)Discoverer of deductive

Geometry • “Father of deductive geometry”• Credited for five theorems• 1) A circle is bisected by any diameter. • 2) The base angles of an Isosceles Triangle are equal.• 3) The angles between two intersecting straight lines

are equal.• 4) Two triangles are congruent if they have

two angles and one side equal.• 5) An angle in a semicircle is a right angle.

Jack S

Bhaskara

• Can be called Bhaskaracharya meaning “Bhaskara the teacher”.• Lived in India.• Famous for number systems and solving

equations which was not achieved in Europe for several centuries.

• More information at

http://www.maths.wichita.edu/~richardson/

Jack S

Hypatia of Alexandria(AD 355 or 370 – 415)

Hypatia’s father (Theon) was a mathematician in Alexandria in Egypt and he taught her about mathematics. From about the year 400 onwards she lectured on mathematics and philosophy. She also studied astronomy and astrology and may have invented astrolabes (which can be used to study astronomy) . However, there is no proof that she did this.

Although she did not make any discoveries herself, she helped her father Theon with some of his works, and was the first woman to make a significant contribution to the development of mathematics.

She was believed by some people to practise magic and was also hated for being a pagan. In AD 415 she was murdered in the street by a group of monks.

The Crater Hypatia and Rimae Hypatia (features of the moon) are both named after Hypatia.

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hypatia.html

Rachel

Julia Hall Bowman Robinson (1919 – 1985)

Julia was born in Missouri in the USA.

When she was nine, she caught scarlet fever, which was followed by rheumatic fever. In total she missed two years of school. Over the next year, she had lessons three mornings a week and managed to get through four years of education (fifth to eighth grades). In her last year at school she was the only girl in her maths and physics classes.

In 1948 she started work on Hilbert’s tenth problem (Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers) and came up with the Robinson hypothesis. This helped Yuri Matijasevic to find the final solution to the problem in 1970.

Rachel

Mary Ann Elizabeth Stephansen(1872 -1961)

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Stephansen.html

She was born in Bergen in Norway on 10 March 1872. She studied at university in Zurich in Switzerland. She was the only Norwegian to pass the entrance exam. When she left in 1896 she became a teacher in Norway, which was unusual for women at that time. During her time as a teacher she also worked on partial differential equations.

In 1906 she was appointed to the Norwegian Agricultural College where she taught maths and physics. She retired in 1931 and went to live with her sister Gerda in England.

Rachel

Hieroglyphic numerals in Egypt - Brought in +/- 3000BC

10,000,000107

1,000,000106

100,000105

10,000104

1,000103

100102

10101

110

Egyptian hieroglyphics were a symbol for each power of 10.

It did not matter if there was a 0 in the number because of the powers.

This is the number 4622

Rosa

Roman Numerals

I V X L C D M___________

V

Symbol = 1

Symbol= 5

Symbol = 10

Symbol = 50

Symbol = 100

Symbol = 500

Symbol = 1000

Symbol = Number times by 1,000 to get the value, in this case 5,000

To get a number you put the symbol’s together in the correct order unless there is a shorter way of writing it…

For Example - To get some numbers you can put a smaller number in front of a larger number indicating a subtraction. E.g. 999 can be written like this… IM which is a lot easier than DCCCCLXXXXVIIII

Roman Numerals are mainly used for writing dates and on clocks

Rosa

John Napier 1550-1617He is most well known for his inventions of logarithms but also invented ‘Napier's bones’ which are a way of multiplying, dividing, and taking square and cube roots.

The board consists off 9 rods which have the times table of 1-9 on each and the number of the corresponding times table at the top

You turned them so at they top it made your number then add the numbers in the row if you are multiplying it by a number with more than one digit you would do it for both add a zero on they tens 2 zeros on the hundreds etc then add together

By Sam allum

Sam

Arabic/Islamic mathematics

Sameer

Arabic mathematics : forgotten brilliance?

Recent research has proved the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries, were actually developed by Arabic/Islamic mathematicians around four centuries earlier! In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks.

The Indian numerals were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe. The story of this transmission is not, however, a simple one. The eastern and western parts of the Arabic world both saw separate developments of Indian numerals with relatively little interaction between the two. By the western part of the Arabic world we mean the regions comprising mainly North Africa and Spain. Transmission to Europe came through this western Arabic route, coming into Europe first through Spain.

Arabic NumeralsSameer

Aristarchus’ Heliocentric Astronomy.

(310BC - BC 210BC)He was a Greek mathematician and an astronomer. He is widely known for proposing the theory that the universe was sun-centred (heliocentric).

He also made some calculations that gave him an estimation of the sizes and the distance of the Sun and the Moon, for example, the volume of Aristarchus's Sun would be almost 300 times greater than the Earth.

Sophie

Ptolemy’s Almagest.

(85AD- 165AD). Claudius Ptolemy put a book together called

Mathematical Compilation. It was a book on everything that people knew about astronomy at the time.

He thought that the Earth was the centre of the universe, but surprisingly the calculations he made were fairly accurate. Up until 1542, Almagest was still the primary source of astronomical knowledge.

Sophie

Johannes Kepler (1571 -1630) Germany

Kepler was a mathematician who studied astronomy. In his book, he gave his first 2 laws of astronomy:

1. The planets move around the Sun in elliptical orbits.

2. The radius vector joining a planet to the sun sweeps out equal areas in equal time.

(1)The orbits are ellipses, with focal

points ƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3 for the second planet. The sun is placed in a fixed point ƒ1.

(2) The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2. (3) The total orbit times for planet 1 and planet 2 have a ratio a13/2 : a23/2.

Isaac Newton later used Kepler’s theory for his gravitational theory.Sruthi

Euclid of Alexandria (325BC – 265BC)

Euclid was a Greek mathematician best

known for his treatise on geometry: The

Elements . This influenced the development

of Western mathematics for more than 2000

years.

Sruthi

Pythagorean Arithmetic and Geometry

• Pythagoras was a Greek philosopher in 500BC. He is best known for discovering the formula for finding the hypotenuse on a right angled triangle, using the other two sides.

• Around 518BC, Pythagoras started a school based on religion and philosophy. The school had many followers, and was to be found in Crotone in Southern Italy. Pythagoras had started another school in Samos, which he abandoned. Pythagoras named his followers the Mathematikoi. They were pure mathematicians. They followed strict rules of respect and humility. They had very few possessions.

Ben

Sieve of Eratosthenes• Eratosthenes was a Greek philosopher, but was also an author,

poet, athlete, geographer, and astronomer. He was the first to calculate the circumference of the Earth.

• Eratosthenes was to first to conceive a method of finding all the prime numbers up to a certain integer. This link explains more; http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes. However, a brief explanation is this;

• 1. Think of a continuous list of numbers from two to some integer.

• 2. Cross out all multiples of two.

• 3. The next lowest, uncrossed number is a prime.

• 4. Cross off all of this number’s multiples.

• 5. Repeat step’s 3 and 4 until you have no more multiples.

Ben

Buffon’s (1777) Needle Problem

Buffon’s needle problem involves probabilities.

A bunch of needles are scattered on a set of parallel lines and we need to find the probability of a needle falling on one of the lines.

The general formula for the probability is

Total Needles= 500 tosses

Red needles/ needles on a line= 107

Probability of crossing in this one is..(107/500)*100= 0.214*100= 21.4%

Vivek

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