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- 1. Maths of nature Patterns, Nature, & Math Are They Interconnected? Mrs. Christi Wilson Greenbrier Middle School अमरनाथ मर्ती ू
- 2. •“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is “ (John Von Neumann)
- 3. "Natural" Patterns Plants Minerals Animals WaterTree Trunk Mushroom Granite Fossils Butterfly Tiger Waves Dew
- 4. Natural beauties
- 5. Natural Intelligence• Some Insects can performs complicated Tasks which is beyond Human beings.• Unknowingly they apply quite advance mathematics.
- 6. spider’s web
- 7. spider’s web
- 8. spider’s web
- 9. spider’s web
- 10. spider’s web
- 11. Spider’s web is 25 times stronger than the same thickness steel wire
- 12. • 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.
- 13. Squarepattern Non Useful empty space
- 14. Hexagonal pattern Non Useful empty space
- 15. The only regular polygons that can cover the plane are triangles, squares and hexagons. 3 sides 4 sides 5 sides 6 sides leaves gaps
- 16. Efficiency Equillateral Triangle Area 0.048 Area of Square 0.063 Area of hexagon 0.075
- 17. Packing Spheres
- 18. Hexagonal packing
- 19. Fibonacci NumbersNature 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.
- 20. Fibonacci “ Leonardo Da vinci”
- 21. 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
- 22. Start with one pair of rabbitsRules of growth1. 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 = ?
- 23. 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, …
- 24. Month Pairs of Rabbits 1 1 2 1 3 2 4 3 5 5
- 25. 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
- 26. Fibonacci’s Rabbit Colony Pairs of Rabbits160 144140120100 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
- 27. New born ---- tenderAdult ---- strongGives birth ----branches out ‘sneezewort’ Eight Five Three Two One One
- 28. <>
- 29. Golden Spiral manipulative
- 30. (Shell)
- 31. The human feotus develops along the lines of a Fibonacci spiral
- 32. Sheep
- 33. Sea Shell Galaxies
- 34. A low pressure area over Iceland showsan approximately logarithmic spiral pattern
- 35. Spirals in the Galaxy
- 36. Rose petals
- 37. Sunflower with 34 petals
- 38. 1 13 Flowers! 2 3 521 8
- 39. euphorbia trilliumwhite calla lily bloodroot black-eyed susan daisy family 13, 21, 34, 55 or 89 petals
- 40. 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…
- 41. Phi = 1.6180339887…• Golden ratio• Golden mean• Golden section• Fibonacci ratio• Divine Ratio• Sacred ratio
- 42. Leaf arrangements
- 43. leaf arrangements 2 1 3 5 6 7 8 9 1 0 12 11 1 15 314 16
- 44. Leaves, petals and seeds arranegment 222.5/137.5 = Φ= 1.6181/Φ =.618 = Φ -1 , 1- 1/Φ = .3820·382x360 = 137·5°
- 45. 12Benefits: 7 15•Moisture 4 10 2 9•Sunlight 1 5•Insects 6 3 14 8 11 13 16
- 46. 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.
- 47. • In a 120 0 arrangement like a fan, 4th one would hide the first leaf
- 48. Why does nature like using Phi in so many plants? • Although hexagonal symmetry is the best packing for circular seeds, it doesnt answer the question of how leaves should be arranged round a stem or how to pack flower-heads with seeds that grow in size.
- 49. 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.
- 50. Pinecones!
- 51. Pine cones pa[na kaona
- 52. Banana Apple
- 53. In vegetable?
- 54. 5 RedSpirals 8 Blue Spirals
- 55. 1 1.618 WHOLEWHOLE = LARGE = GOLDEN MEANLARGE SMALL
- 56. Human Hand
- 57. DNA
- 58. Beautiful Facial StructuresDr. Marquadt’s perfect face mask
- 59. • 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.
- 60. Leonardo Da Vinci, Mona
- 61. सर्व धमव समभार् Symbol
- 62. Musical instruments are often based on phi
- 63. • 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.
- 64. Golden mean gauge
- 65. The Bagdad City Gate
- 66. Dome of St. Paul:London, England
- 67. Windson Castle
- 68. Golden Caliper
- 69. ART MUSIC AdvertisementArchitecture
- 70. Shape of Universe
- 71. Rings of Saturn
- 72. 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.
- 73. Great Pyramids
- 74. Egyptians in the design of the pyramids,
- 75. The CN Tower inToronto, the tallesttower.The ratio of observationdeck at 342 meters tothe total height of553.33 is 0.618, thereciprocal of Phi!
- 76. Notre Dame in Paris
- 77. 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.
- 78. 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
- 79. Φ Is an Infinite Square Root 1 1 1 1 .....
- 80. Φ as a Continued Fraction 1 1 1 1 1 1 1 1 ... 1
- 81. Fibonacci numbers define key points in human aging DevelopmentHuma Key Attributes Stagen 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
- 82. Fibonacci numbers define key points in human aging DevelopmentHuman Key Attributes StageAge 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
- 83. Surely it is logical to concludethat the connections existbecause nature, mathematicsand the human mind, with itssubtle sense of beauty, have onesupreme link — they are all thecreated products of God, theMaster Designer
- 84. Phi•No rational approximation for long• e = 2.71828..... ≈ 2+ 5/7 → 7 arms•π = 3.141592… ≈ 3 + 1/7 → 7 arms1+ 1 1+ 1 1+ 1 1+ 1 1+…
- 85. 2 1 28 5
- 86. Da Vinci Code
- 87. Salary TheoremThe 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.
- 88. Salary TheoremThe 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.
- 89. 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.
- 90. • 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, theres 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 doesnt need.
- 91. • 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 doesnt.• A man marries a woman expecting that she wont 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 doesnt understand a woman - before marriage and after marriage.
- 92. 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
- 93. Girl is absolute eveil
- 94. 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
- 95. • 1000 SUM THE NUMBERS AS THEY ARE AND NOT DIGIT- VICE THE SUM IS 10000
- 96. • 1000• 3000 SUM THE NUMBERS AS THEY ARE AND NOT DIGIT-VICE IS THE SUM 10000?
- 97. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE IS THE SUM 10000?
- 98. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000 IS THE SUM 10000?
- 99. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?
- 100. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000
- 101. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000
- 102. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000• 0020
- 103. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000• 0020
- 104. Rounding off Psycology•TOTAL•10000 OR 9100?

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