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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
The
Greeks
The
Chinese
The
Indians
The Arabs
Beauty: What do we define it to
be?
The quality present in a thing orperson that
gives intense pleasure ordeep satisfactio...
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...
Mathematics and Physical
Beauty
 Why do we find people to be attractive?
 Because the proportions of the length
of the n...
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, 6...
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...
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, spiral...
Mathematics and Architecture
In ancient times architecture was a field of mathematics.
Architects were simply mathematicia...
Mathematics and Architecture
Both areas search for order
and beauty- Mathematics
in nature and architecture
in constructio...
Mathematics and Architecture
The tallest building in the world:
The Burj Khalifa in Dubai.
Very tall buildings are in dang...
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
ourown 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 t...
Mathematicians – believe it or not, we are
human!
Galois Nash
Noether
Newton
Germain
Gauss
Einstein
Green
Mathematicians – our minds
Mathematicians – our minds
Mathematicians – our minds
Numbers are to
mathematics what
words are to language.
To the ‘distress’ of the
general society...
Mathematics in life - numbers
The first securely datable
Mathematical Table in World
History, circa 2600 BCE was
developed by the Sumerians, in
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-S...
Completing the Square
Incomplete square Completed square
6x ?
x2
6x
x
6 6x 6622
6xx2
6x
?
RESOURCES TO TEACH
MATHEMATICS
WHY ARE WE DOING
ALL OF THIS?
WHERE DO WE GO
FROMHERE?
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
The beauty of mathematics
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The beauty of mathematics

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The beauty of mathematics

  1. 1. THE BEAUTY AND REALITY OF MATHEMATICS
  2. 2. HEARTFELT THANKS TO THOSE BEFORE US……..WITH US NOW…………AND TO COME ALL THE GIFTS HAVE MADE LIFE BETTER
  3. 3. The Sumerians The The Greeks The Chinese The Indians The Arabs
  4. 4. 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).
  5. 5. Chaos Theory
  6. 6. Fractals – the delight of Chaos Theory. A fractal expression looks like Z = Fn1(Z); Z = Z*Z + Fn2(C)
  7. 7. Mathematics and Physical Beauty
  8. 8. 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)
  9. 9. 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.
  10. 10. The Golden Ratio
  11. 11. 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.
  12. 12. Where did 1.6180339887……. come from? Let’s look at the ratio of each number in The Fibonacci sequence to the one before it:
  13. 13. 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.
  14. 14. The Golden Ratio: Some Other Examples
  15. 15. The Golden Ratio: Some Other Examples
  16. 16. 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
  17. 17. 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.
  18. 18. Mathematics and Architecture Both areas search for order and beauty- Mathematics in nature and architecture in construction.
  19. 19. 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.
  20. 20. Mathematics and Architecture Some are purely utilitarian such as the Great Wall of China.
  21. 21. Mathematics and Architecture Some failed miserably and provide us with mirth and wonder.
  22. 22. Mathematics and Architecture  The Alhambra Palace in Andalucia, Spain  Building started in 1238 Watch
  23. 23. Mathematics and Architecture Not to be outdone, we have ourown styles.
  24. 24. Topology – Some Games
  25. 25. Answers
  26. 26. 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.
  27. 27. Mathematicians – believe it or not, we are human! Galois Nash Noether Newton Germain Gauss Einstein Green
  28. 28. Mathematicians – our minds
  29. 29. Mathematicians – our minds
  30. 30. 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.
  31. 31. Mathematics in life - numbers
  32. 32. The first securely datable Mathematical Table in World History, circa 2600 BCE was developed by the Sumerians, in
  33. 33. Ye Gads!!! Algebra!!!
  34. 34. THE DISTRIBUTIVE PROPERTY y z x
  35. 35. 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
  36. 36. 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
  37. 37. Completing the Square Incomplete square Completed square 6x ? x2 6x x 6 6x 6622 6xx2 6x ?
  38. 38. RESOURCES TO TEACH MATHEMATICS
  39. 39. WHY ARE WE DOING ALL OF THIS? WHERE DO WE GO FROMHERE?

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