The beauty of mathematics

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
Greek
s

The Sumerians
The

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



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 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 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


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 beautyMathematics in nature
and architecture in



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


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