The whole world is designed on mathematical lines and nature behaves mathematically . This presentatin brings out natures beauty as optimal mathematical design

2. Maths of nature
Patterns, Nature, & Math
Are They Interconnected?
Mrs. Christi Wilson
Greenbrier Middle School
अमरनाथ मर्ती
ू

3. •“If people do not believe
that mathematics is simple,
it is only because they do
not realize how
complicated life is “
(John Von Neumann)

4. "Natural" Patterns
Plants Minerals Animals Water
Tree Trunk Mushroom Granite Fossils Butterfly Tiger Waves Dew

5. Natural beauties

8. Natural Intelligence
• Some Insects can performs
complicated Tasks which is
beyond Human beings.
• Unknowingly they apply quite
advance mathematics.

10. spider’s web

11. spider’s web

12. spider’s web

13. spider’s web

14. spider’s web

15. Spider’s web is 25 times stronger than
the same thickness steel wire

17. • Termites air-conditioned
mound with chimney.
• It is an Engineering
Marvel.
• Up to 30 feet high.
• CO2 /O2 balance .
• Inside these mounds are
“gardens” where
termites grow their food
called fungus.

24. Square
pattern
Non Useful
empty space

25. Hexagonal pattern
Non Useful
empty space

26. The only regular polygons that can cover the
plane are triangles, squares and hexagons.
3 sides 4 sides 5 sides 6 sides
leaves gaps

27. Efficiency
Equillateral
Triangle Area
0.048
Area of Square
0.063
Area of hexagon
0.075

28. Packing Spheres

29. Hexagonal packing

30. Fibonacci Numbers
Nature has it’s own Number
System called Fibonacci
number system which is
applicable to all those things
which take birth and grow or
grow otherwise ; almost all
aspects of life.

31. Fibonacci “ Leonardo Da vinci”

32. Role of Fibonacci numbers
• Trees , Plants, leaves, flowers, stems
• Bee Hive, spider’s web
• Human Body
• Various insects and Animals
• music, art, Culture, and Science
• Business, Ads, and share market

33. Start with one pair of rabbits
Rules of growth
1. Every new born pair becomes adult in
one month.
2. Every adult pair after one month gives
birth to one pair every month.
3. No rabbit dies.
population of rabbits after one year = ?

34. Modelization of a population
Adult pairs Young pairs
• First month
• Secod month
• third month
• Fourth month
• Fifth month
• Sixth month
Sequence: 1, 1, 2, 3, 5, 8, …

36. Month Pairs of Rabbits
1 1
2 1
3 2
4 3
5 5

37. Fibonacci Series
• The rule for the sequence?
1, 1, 2, 3, ?, ?, ….
• The Answer :
1, 1, 2, 3, 5, 8, 13, 21, …
1+ 1 = 2+ 33= 5 = 8 = 13 = 21
1+ 2 = 3+ 5 8+ 13
5+
Fn+1= Fn + Fn-1

38. Fibonacci’s Rabbit Colony
Pairs of Rabbits
160 144
140
120
100 89
80
60 55
40 34
13 21
20 1 1 2 3 5 8
0
March
April
August
June
May
October
November
December
July
September
January
February

41. New born ---- tender
Adult ---- strong
Gives birth ----branches out
‘sneezewort’
Eight
Five
Three
Two
One
One

43. <>

44. Golden Spiral manipulative

47. (Shell)

50. The human feotus develops along the lines of a Fibonacci spiral

51. Sheep

54. Sea Shell
Galaxies

55. A low pressure area over Iceland shows
an approximately logarithmic spiral pattern

56. Spirals in the Galaxy

58. Rose petals

60. Sunflower with 34 petals

61. 1 13
Flowers!
2
3
5
21 8

62. euphorbia trillium
white calla lily
bloodroot black-eyed susan
daisy family
13, 21, 34, 55
or 89 petals

63. 1, 1 ,2 ,3 ,5 ,8 ,13 ,21 ,34 ,55 ,…
1/1, 2/1, 3/2, 5/3, 8/5, 13/8…
1, 2, 1.5, 1.666, 1.6, 1.625, …
Golden ratio
 phi = 1.6180339887…

65. Phi = 1.6180339887…
• Golden ratio
• Golden mean
• Golden section
• Fibonacci ratio
• Divine Ratio
• Sacred ratio

66. Leaf arrangements

68. leaf arrangements
2
1 3 5
6 7
8
9
1
0
12
11
1
15 3
1
4
16

70. Leaves, petals and
seeds arranegment
222.5/137.5 = Φ= 1.618
1/Φ =.618 = Φ -1 , 1- 1/Φ = .382
0·382x360 = 137·5°

71. 12
Benefits: 7 15
•Moisture 4 10
2
9
•Sunlight
1 5
•Insects
6 3
14
8
11 13
16

72. Leaf arrangements
• If we look down on a plant, the leaves
are often arranged so that leaves
above do not hide leaves below.
• Each gets a good share of the sunlight
and catches the most rain to channel
down to the roots as it runs down the
leaf to the stem.
• Insects can collect pollens easily.

73. • In a 120 0 arrangement like a fan,
4th one would hide the first leaf

74. Why does nature like using Phi in so many plants?
• Although hexagonal symmetry is the
best packing for circular seeds, it
doesn't answer the question of how
leaves should be arranged round a
stem or how to pack flower-heads
with seeds that grow in size.

78. Left to right: A sunflower picture from The Algorithmic Beauty of Plants, P.
Prusinkiewicz. A cactus by C. Smith. Another Cactus by C. Smith and M.
Fuhrer.

83. Pinecones!

84. Pine cones pa[na kaona

87. Banana Apple

88. In vegetable?

91. 5
Red
Spirals
8
Blue
Spirals

94. 1 1.618
WHOLE
WHOLE = LARGE = GOLDEN MEAN
LARGE SMALL

97. Human Hand

99. DNA

102. Beautiful Facial Structures
Dr. Marquadt’s perfect face mask

103. • Dr. Stephen
Marquardt, a former
plastic surgeon, has
used the golden
section, that
enigmatic number
that has long stood for
beauty, and some of
its relatives to make a
mask that he claims is
the most beautiful
shape a human face
can have.

107. Leonardo Da Vinci, Mona

115. सर्व धमव समभार्
Symbol

116. Musical instruments are often based
on phi

117. • Musical scales are based on Fibonacci
numbers;
piano keyboard scale of 13 keys has 8
white keys and 5 black keys, split into
groups of 3 and 2.

118. Golden mean gauge

125. The Bagdad City Gate

126. Dome of St. Paul:
London, England

127. Windson Castle

142. Golden Caliper

143. ART
MUSIC
Advertisement
Architecture

146. Shape of Universe

148. Rings of Saturn

150. Further classic subdivisions of the rectangle
align perfectly with major architectural features
of the structure.
Further classic subdivisions of the rectangle align perfectly with major architectural features of the structure.

151. Great Pyramids

152. Egyptians in the design of the pyramids,

154. The CN Tower in
Toronto, the tallest
tower.
The ratio of observation
deck at 342 meters to
the total height of
553.33 is 0.618, the
reciprocal of Phi!

155. Notre Dame in Paris

168. Human expectations occur
in a ratio that approaches Phi
• our brains are hardwired to find Fibonacci
progressions naturally pleasing.
• Changes in stock prices largely reflect human
opinions, valuations and
expectations. Humans exhibit positive and
negative evaluations of the opinions they hold
in a ratio that approaches phi, with 61.8%
positive and 38.2% negative.
• Used to predicting stock market behaviour.

169. Fibonacci (downward) Retracement with continuing upward trend
a 23.6%
38.2%
b 50%%
61.8%
• a/b ratios : 23.6%, 38.2%, 50%, 61.8%
• When Fibonacci behavior applies, price “a” may drop 23.6%
of “b”, or 38.2%, or 50%, or 61.8%, before it continues its
upward trend.
• This is used as an investment guide

170. Φ Is an Infinite Square Root
  1  1  1  1  .....

171. Φ as a Continued Fraction
1
  1
1
1
1
1
1
1  ...
1

172. Fibonacci numbers define key points in human aging
Development
Huma Key Attributes
Stage
n Age
0 Gestation Conception
1 Newborn Birth
1 Infant Walking, vocalizing
2 Toddler Talking, expressing, imitating
Self image and control, toilet
3 Toddler
training
5 Early child Formal education begins
Age of reason, knowing of right
8 Mid child
and wrong

173. Fibonacci numbers define key points in human aging
Development
Human Key Attributes
Stage
Age
Thinking, puberty, sexual
13 Adolescent
maturation and drive
Full physical growth, adult in
society, education complete,
Young
21 beginning career, financial
adult
responsibility, eligible for
voting
Refinement of adult skills,
34 Mid adult
parenting role
Fulfillment of adult skills,
serving, retirement begins with
55 Elder adult
eligibility for Medicare, Social
Security

174. Surely it is logical to conclude
that the connections exist
because nature, mathematics
and the human mind, with its
subtle sense of beauty, have one
supreme link — they are all the
created products of God, the
Master Designer

177. Phi
•No rational approximation for long
• e = 2.71828..... ≈ 2+ 5/7 → 7 arms
•π = 3.141592… ≈ 3 + 1/7 → 7 arms
1+ 1
1+ 1
1+ 1
1+ 1
1+…

178. 2
1
2
8 5

181. Da Vinci Code

183. Salary Theorem
The less you know, the more you make.
Proof:
• Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows:
• Power = Work / Time
And since
• Knowledge = Power and Time = Money
therefore
• Knowledge = Work / Money .
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches
infinity, regardless of the amount of Work done.

184. Salary Theorem
The less you know, the more you make.
Proof:
• Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows:
• Power = Work / Time
And since
• Knowledge = Power and Time = Money
therefore
• Knowledge = Work / Money .
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches
infinity, regardless of the amount of Work done.

185. GENERAL EQUATIONS & STATISTICS
• A woman worries about the future until she gets a
husband.
• A man never worries about the future until he gets
a wife.
• A successful man is one who makes more money
than his wife can spend.
• A successful woman is one who can find such a
man.
• To be happy with a man, you must understand him
a lot and love him a little.

186. • To be happy with a woman, you must love her
a lot and not try to understand her at all.
• Married men live longer than single men, but
married men are a lot more willing to die.
• Any married man should forget his mistakes,
there's no use in two people remembering the
same thing
• SHOPPING MATH
• A man will pay $2 for a $1 item he needs. A
woman will pay $1 for a $2 item that she
doesn't need.

187. • Men wake up as good-looking as they went to bed.
Women somehow deteriorate during the night.
• A woman marries a man expecting he will change,
but he doesn't.
• A man marries a woman expecting that she won't
change, and she does.
• A woman has the last word in any argument.
Anything a man says after that is the beginning of a
new argument.
• There are 2 times when a man doesn't understand a
woman - before marriage and after marriage.

188. ROMANCE MATHEMATICS
• Smart man + smart woman = romance
• Smart man + dumb woman = affair
• Dumb man + smart woman = marriage
• Dumb man + dumb woman = pregnancy
•
OFFICE ARITHMETIC
• Smart boss + smart employee = profit
• Smart boss + dumb employee = production
• Dumb boss + smart employee = promotion
• Dumb boss + dumb employee = overtime

190. Girl is absolute eveil

191. AaOrt = baura[-yaa^M
• AaOrt = samaya X Qana
• samaya = Qana Aqaa-t AaOrt = Qana 2
• Qana = baura[-yaaoM ka maUla
(money is the root of all evil)
• AaOrt = Qana 2
• AaOrt = ( baura[-yaaoM ka maUla ) 2
• AaOrt = baura[-yaa^M

193. • 1000
SUM THE
NUMBERS
AS THEY ARE
AND NOT DIGIT-
VICE
THE SUM IS
10000

194. • 1000
• 3000 SUM THE NUMBERS
AS THEY ARE
AND NOT DIGIT-VICE
IS THE SUM 10000?

195. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
IS THE SUM 10000?

196. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
IS THE SUM 10000?

197. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
• 0030 IS THE SUM 10000?

198. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
• 0030 IS THE SUM 10000?
• 1000

199. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
• 0030 IS THE SUM 10000?
• 1000
• 1000

200. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
• 0030 IS THE SUM 10000?
• 1000
• 1000
• 0020

201. • 1000
• 3000 SUM THE NUMBERS
• 0050 AS THEY ARE
AND NOT DIGIT-VICE
• 3000
• 0030 IS THE SUM 10000?
• 1000
• 1000
• 0020

202. Rounding off Psycology
•TOTAL
•10000 OR 9100?