This document provides an overview of mathematics and its relationship to concepts of beauty, architecture, and human life. It discusses how mathematical patterns like the golden ratio and Fibonacci sequence are found in nature and influence concepts of beauty. It also explores how mathematics influenced ancient architecture and how geometry guides both fields. Additionally, it examines how mathematicians think and how numbers are fundamental to mathematics, similar to how words are to language. The document aims to convey the breadth of mathematics and its applications beyond numerical calculations.

1. THE
BEAUTY AND
REALITY
OF MATHEMATICS

2. HEARTFELT THANKS TO
THOSE BEFORE
US……..WITH US
NOW…………AND TO COME
ALL THE GIFTS HAVE MADE
LIFE BETTER

3. The Sumerians The
The
Greeks
The
Chinese
The
Indians
The Arabs

5. Beauty: What do we define it to
be?
The quality present in a thing orperson that
gives intense pleasure ordeep satisfaction
to the mind, whetherarising fromsensory
manifestations (as shape, colour, sound,
etc.), a meaningful design orpattern, or
something else (as a personality in
which high spiritual qualities are manifest).

6. Chaos
Theory

7. Fractals – the delight of Chaos Theory.
A fractal expression looks like Z = Fn1(Z); Z = Z*Z + Fn2(C)

8. Mathematics and Physical
Beauty

10. 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)

11. 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.

13. The Golden Ratio

14. 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.

15. Where did 1.6180339887……. come from?
Let’s look at the ratio of each number in The Fibonacci
sequence to the one before it:

16. 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.

17. The Golden Ratio: Some Other
Examples

18. The Golden Ratio: Some Other
Examples

19. 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

20. 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.

22. Mathematics and Architecture
Both areas search for order
and beauty- Mathematics
in nature and architecture
in construction.

24. 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.

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

26. Mathematics and Architecture
Some failed miserably and
provide us with mirth and
wonder.

28. Mathematics and Architecture
 The Alhambra Palace
in Andalucia, Spain
 Building started in
1238
Watch

29. Mathematics and Architecture
Not to be
outdone, we have
ourown styles.

30. Topology – Some Games

31. Answers

32. 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 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 o
5 + 1 + 5 + 9 + 1 + 6 = 27 = 9
So this persons soul urge number is 9 and they can go read up about
their personality.

33. Mathematicians – believe it or not, we are
human!
Galois Nash
Noether
Newton
Germain
Gauss
Einstein
Green

34. Mathematicians – our minds

35. Mathematicians – our minds

36. 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.

37. Mathematics in life - numbers

39. The first securely datable
Mathematical Table in World
History, circa 2600 BCE was
developed by the Sumerians, in

40. Ye Gads!!! Algebra!!!

42. THE DISTRIBUTIVE PROPERTY
y z
x

43. 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

44. 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

45. Completing the Square
Incomplete square Completed square
6x ?
x2
6x
x
6 6x 6622
6xx2
6x
?

46. RESOURCES TO TEACH
MATHEMATICS

47. WHY ARE WE DOING
ALL OF THIS?
WHERE DO WE GO
FROMHERE?