THE BEAUTY AND

REALITY OF MATHEMATICS

HEARTFELT THANKS TO THOSE BEFORE US……..WITH US

NOW…………AND TO COME

ALL THE GIFTS HAVE MADE LIFE BETTER

The SumeriansThe Egyptians

The Greeks

The ChineseThe Indians

The Arabs

Beauty: What do we define it to be?

The quality present in a thing or person that gives intense pleasure or deep satisfaction to the mind, whether

arising from sensory manifestations (as shape, colour, sound, etc.), a meaningful design or pattern, or something else (as

a personality in which high spiritual qualities are manifest).

Chaos Theory

Fractals – the delight of Chaos Theory.

A fractal expression looks like Z = Fn1(Z); Z = Z*Z + Fn2(C)

Mathematics and Physical Beauty

Mathematics and Physical Beauty

Leonardo da Vinci's drawings of the human body emphasised its proportion. The ratio of the following distances is the Golden Ratio: (foot to navel) : (navel to head)

Mathematics and Physical Beauty

Why do we find people to be attractive?

Because the proportions of the length of the nose, the position of the eyes and the length of the chin all conform to some aspect of the Golden Ratio.

The Golden Ratio

The Fibonacci Sequence: the first 20

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765.

Where did 1.6180339887……. come from?

Let’s look at the ratio of each number in The Fibonacci sequence to the one before it:

The Golden RatioMeasure the length and width of your face. Divide the length by the width. This should give approximately 1.6, which means a beautiful person’s face is about 11/2 times longer than it is wide.

The Golden Ratio: Some Other Examples

The Golden Ratio: Some Other Examples

The Golden Ratio: Some Other Examples

In seed heads such as the sunflower shown here and the coneflower previously, spirals curve left and right. The number of spirals curving left and the number of spirals curving right are neighbours in the Fibonacci sequence, for example, the number of spirals curving left is 34 and the number of spirals curving right is 55.

Mathematics and Architecture

In ancient times architecture was a field of mathematics.Architects were simply mathematicians that someone

would hire.Geometry is the guiding principle between the two areas.

Mathematics, however, is indispensible to the understanding of structural concepts and calculations.

Mathematics and Architecture

Both areas search for order and beauty-

Mathematics in nature and architecture in

construction.

Mathematics and Architecture

The tallest building in the world:The Burj Khalifa in Dubai.

Very tall buildings are in danger of many things depending on where they are. Stability against earthquakes is important as well as ensuring aerodynamic designing is done perfectly to mitigate against swaying.

Mathematics and Architecture

Some are purely utilitarian such as the Great Wall of China.

Mathematics and Architecture

Some failed miserably and provide us with mirth

and wonder.

Mathematics and Architecture

The Alhambra Palace in Andalucia, Spain

Building started in 1238Watch

Mathematics and Architecture

Not to be outdone, we have our own styles.

Topology – Some Games

Answers

NumerologyIt has always been, and still is the desire to understand people and ourselves. Numbers were used a very long time ago, in the absence of more scientific means, to tell of one’s personality and future. In this example we look at calculating the Soul Urge Number.

Write out your full birth name (this includes your middle name (s). Using only the vowels in your name, assign these values:A = 1, E = 5, I = 9, O = 6 and U = 3.

Example: Heather Ina Brown, the vowels are eae ia o5 + 1 + 5 + 9 + 1 + 6 = 27 = 9So this persons soul urge number is 9 and they can go read up about their personality.

Mathematicians – believe it or not, we are human!

Galois NashNoetherNewtonGermainGaussEinsteinGreen

Mathematicians – our minds

Mathematicians – our minds

Mathematicians – our mindsNumbers are to mathematics what words are to language.To the ‘distress’ of the general society mathematicians have ‘dreamt’ up types of numbers.

Mathematics in life - numbers

The first securely datable

Mathematical Table in

World History, circa 2600

BCE was developed by the

Sumerians, in ancient

African Tribe.

Ye Gads!!! Algebra!!!

THE DISTRIBUTIVE PROPERTY

y z

x

Area = (x+4)(5+x) = (x+4)5 +(x+4)x = 5x+20+x2+4x = x2+9x+20

5 x

x+4 (x+4)5 (x+4)x

ba

a

b ab b2

aba2

You can see from the diagram that the area of the large square is both (a+b)2 and a2 +2ab+b2 .

Perfect-Square Trinomials

Completing the SquareIncomplete square Completed square

x2 +12x x2 +12x +6622 6x ?

x2

6x

x

6 6x 6622

6xx2

6x

?

RESOURCES TO TEACH MATHEMATICS

WHY ARE WE DOING ALL OF

THIS?

WHERE DO WE GO FROM HERE?