Maths and nature english

862 views
703 views

Published on

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

0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
862
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
9
Comments
0
Likes
3
Embeds 0
No embeds

No notes for slide

Maths and nature english

  1. 1. Maths of nature Patterns, Nature, & Math Are They Interconnected? Mrs. Christi Wilson Greenbrier Middle School अमरनाथ मर्ती ू
  2. 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. 3. "Natural" Patterns Plants Minerals Animals WaterTree Trunk Mushroom Granite Fossils Butterfly Tiger Waves Dew
  4. 4. Natural beauties
  5. 5. Natural Intelligence• Some Insects can performs complicated Tasks which is beyond Human beings.• Unknowingly they apply quite advance mathematics.
  6. 6. spider’s web
  7. 7. spider’s web
  8. 8. spider’s web
  9. 9. spider’s web
  10. 10. spider’s web
  11. 11. Spider’s web is 25 times stronger than the same thickness steel wire
  12. 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. 13. Squarepattern Non Useful empty space
  14. 14. Hexagonal pattern Non Useful empty space
  15. 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. 16. Efficiency Equillateral Triangle Area 0.048 Area of Square 0.063 Area of hexagon 0.075
  17. 17. Packing Spheres
  18. 18. Hexagonal packing
  19. 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. 20. Fibonacci “ Leonardo Da vinci”
  21. 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. 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. 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. 24. Month Pairs of Rabbits 1 1 2 1 3 2 4 3 5 5
  25. 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. 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. 27. New born ---- tenderAdult ---- strongGives birth ----branches out ‘sneezewort’ Eight Five Three Two One One
  28. 28. <>
  29. 29. Golden Spiral manipulative
  30. 30. (Shell)
  31. 31. The human feotus develops along the lines of a Fibonacci spiral
  32. 32. Sheep
  33. 33. Sea Shell Galaxies
  34. 34. A low pressure area over Iceland showsan approximately logarithmic spiral pattern
  35. 35. Spirals in the Galaxy
  36. 36. Rose petals
  37. 37. Sunflower with 34 petals
  38. 38. 1 13 Flowers! 2 3 521 8
  39. 39. euphorbia trilliumwhite calla lily bloodroot black-eyed susan daisy family 13, 21, 34, 55 or 89 petals
  40. 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. 41. Phi = 1.6180339887…• Golden ratio• Golden mean• Golden section• Fibonacci ratio• Divine Ratio• Sacred ratio
  42. 42. Leaf arrangements
  43. 43. leaf arrangements 2 1 3 5 6 7 8 9 1 0 12 11 1 15 314 16
  44. 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. 45. 12Benefits: 7 15•Moisture 4 10 2 9•Sunlight 1 5•Insects 6 3 14 8 11 13 16
  46. 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. 47. • In a 120 0 arrangement like a fan, 4th one would hide the first leaf
  48. 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. 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. 50. Pinecones!
  51. 51. Pine cones pa[na kaona
  52. 52. Banana Apple
  53. 53. In vegetable?
  54. 54. 5 RedSpirals 8 Blue Spirals
  55. 55. 1 1.618 WHOLEWHOLE = LARGE = GOLDEN MEANLARGE SMALL
  56. 56. Human Hand
  57. 57. DNA
  58. 58. Beautiful Facial StructuresDr. Marquadt’s perfect face mask
  59. 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. 60. Leonardo Da Vinci, Mona
  61. 61. सर्व धमव समभार् Symbol
  62. 62. Musical instruments are often based on phi
  63. 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. 64. Golden mean gauge
  65. 65. The Bagdad City Gate
  66. 66. Dome of St. Paul:London, England
  67. 67. Windson Castle
  68. 68. Golden Caliper
  69. 69. ART MUSIC AdvertisementArchitecture
  70. 70. Shape of Universe
  71. 71. Rings of Saturn
  72. 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. 73. Great Pyramids
  74. 74. Egyptians in the design of the pyramids,
  75. 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. 76. Notre Dame in Paris
  77. 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. 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. 79. Φ Is an Infinite Square Root  1  1  1  1  .....
  80. 80. Φ as a Continued Fraction 1   1 1 1 1 1 1 1  ... 1
  81. 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. 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. 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. 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. 85. 2 1 28 5
  86. 86. Da Vinci Code
  87. 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. 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. 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. 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. 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. 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. 93. Girl is absolute eveil
  94. 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. 95. • 1000 SUM THE NUMBERS AS THEY ARE AND NOT DIGIT- VICE THE SUM IS 10000
  96. 96. • 1000• 3000 SUM THE NUMBERS AS THEY ARE AND NOT DIGIT-VICE IS THE SUM 10000?
  97. 97. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE IS THE SUM 10000?
  98. 98. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000 IS THE SUM 10000?
  99. 99. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?
  100. 100. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000
  101. 101. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000
  102. 102. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000• 0020
  103. 103. • 1000• 3000 SUM THE NUMBERS• 0050 AS THEY ARE AND NOT DIGIT-VICE• 3000• 0030 IS THE SUM 10000?• 1000• 1000• 0020
  104. 104. Rounding off Psycology•TOTAL•10000 OR 9100?

×