The beauty and reality of mathematics

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The beauty and reality of mathematics
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HEARTFELT THANKS TO THOSE BEFORE US..WITH US
NOWAND TO COME ALL THE GIFTS HAVE MADE
LIFE BETTER
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The Greeks
The Chinese
The Indians
The Sumerians
The Egyptians
The Arabs
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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).

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Chaos Theory
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Fractals the delight of Chaos Theory.
A fractal expression looks like Z Fn1(Z) Z
ZZ Fn2(C)
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Mathematics and Physical Beauty
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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)

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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.

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The Golden Ratio
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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.
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Where did 1.6180339887. come from?
Lets look at the ratio of each number in The
Fibonacci sequence to the one before it
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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.
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The Golden Ratio Some Other Examples
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The Golden Ratio Some Other Examples
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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.
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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.
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Mathematics and Architecture
Both areas search for order and beauty-
Mathematics in nature and architecture in
construction.
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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.
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Mathematics and Architecture
Some are purely utilitarian such as the Great
Wall of China.
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Mathematics and Architecture

• Some failed miserably and provide us with mirth
  and wonder.

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Mathematics and Architecture

• The Alhambra Palace in Andalucia, Spain
• Building started in 1238

Watch
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Mathematics and Architecture
Not to be outdone, we have our own styles.
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Topology Some Games
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Answers
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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 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.
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Mathematicians believe it or not, we are human!
Galois Nash Noether Newton Germain Gauss Einstei
n Green
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Mathematicians our minds
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Mathematicians our minds
 
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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.
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Mathematics in life - numbers
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The first securely datable Mathematical Table in
World History, circa 2600 BCE was developed by
the Sumerians, in ancient African Tribe.
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Ye Gads!!! Algebra!!!
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THE DISTRIBUTIVE PROPERTY
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Area (x4)(5x) (x4)5 (x4)x
5x20x24x x29x20

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Perfect-Square Trinomials

• You can see from the diagram that the area of the
  large square is both (ab)2 and a2 2abb2 .

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Completing the Square

• Incomplete square Completed square
• x2 12x x2 12x 62

6x
?
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RESOURCES TO TEACH MATHEMATICS
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WHY ARE WE DOING ALL OF THIS? WHERE DO WE GO
FROM HERE?