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 Sumerians The Egyptians The Greeks The Chinese The 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

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 ……. come from? Lets look at the ratio of each number in The Fibonacci sequence to the one before it:

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

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 1238 Watch

Mathematics and Architecture Not to be outdone, we have our own styles.

Topology – Some Games

Answers

Numerology It 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 ones 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 o = 27 = 9 So 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 Nash Noether Newton Germain Gauss Einstein Green

Mathematicians – our minds

Numbers 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+x 2 +4x = x 2 +9x+20 5 x x+4 (x+4)5 (x+4)x

b a a b ab b2b2 a2a2 You can see from the diagram that the area of the large square is both ( a+b ) 2 and a 2 +2ab+b 2. Perfect-Square Trinomials

Completing the Square Incomplete squareCompleted square 6 2 x x x x x ? x2x2 6 x x x2x2 ?

RESOURCES TO TEACH MATHEMATICS

WHY ARE WE DOING ALL OF THIS? WHERE DO WE GO FROM HERE?