1. Patterns, Nature, & MathAre They Interconnected? Mrs. Christi WilsonGreenbrier Middle School

2. . 3. "Natural" PatternsPlants MineralsAnimalsWater Tree Trunk Mushroom Granite Fossils Butterfly Tiger WavesDew 4. 5. . , 6. 7. 8. 9. 10. 11. 25 12. 30 . CO2 /O2 . 13. 14. 15. 16. 17. Hexagonal pattern 18. , 3 4 5 6 19. 0.048 0.063 0.075 20. 21. 22. . . 23. 24. , , , , 25. Rules of growth1. .2. .3. . ? 26. : 1, 1, 2, 3, 5, 8, 27. 28. 1 1 2 1 3 2 4 3 5 5 29. ? 1, 1, 2, 3, ?, ?, .1, 1, 2, 3, 5, 8, 13, 21, 1+ 1 = 2+ 33= 5 = 8 = 13 = 211+ 2 = 3+ 5 8+ 13 5+Fn+1= Fn + Fn-1 30. Pairs of Rabbits160144140120100 89 80 6055 40 3413 21 20 1 1 2 3 5 80 March April August June MayOctoberNovember DecemberJulySeptemberJanuaryFebruary 31. ---- ---- ---- sneezewort 32. 33. Golden Spiral manipulative 34. () 35. 36. 37. 38. 39. 40. 41. 34 42. 13 !1 2 3 521 8 43. euphorbia trilliumwhite calla lily bloodrootblack-eyed susan 13, 21, 34, 55 89 44. 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 45. Phi = 1.6180339887 Golden ratio Golden mean Golden section Fibonacci ratio Divine Ratio Sacred ratio 46. 47. 2 1 3 567 8 91012111 15 314 16 48. , 222.5/137.5 = = 1.6181/ =.618 = -1 , 1- 1/ = .3820382x360 = 1375 49. 12:7 15 4 102 9 15 6 3 14811 13 16 50. . . 51. 120 . 52. ? . 53. 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. 54. Pinecones! 55. Pine cones 56. 57. ? 58. 5 8 59. 1 1.618 WHOLE = = 60. 61. 62. 63. 64. , . 65. , 66. ( ) 67. Symbol 68. 69. , , , . . 13 8 5 3 2 . 70. Golden mean gauge 71. The Bagdad City Gate 72. Dome ofSt. Paul:London,England 73. Windson Castle 74. Golden Caliper 75. ART MUSIC AdvertisementArchitecture 76. 77. 78. Further classic subdivisions of the rectangle align perfectly with major architectural features of the structure. 79. 80. Egyptians in the design of the pyramids, 81. . 553.33 342 1.618 82. Notre Dame in Paris 83. . 61.8% 38.2% 84. 1 1 1 1 ..... 85. 1 11 1111 1 ...1 86. Fibonacci numbers define key points in human agingDevelopmentHumaKey AttributesStagen Age0 Gestation Conception1 Newborn Birth1 InfantWalking, vocalizing2 Toddler Talking, expressing, imitatingSelf image and control, toilet3 Toddlertraining5 Early child Formal education beginsAge of reason, knowing of right8 Mid childand wrong 87. Fibonacci numbers define key points in human agingDevelopmentHuman Key AttributesStageAgeThinking, puberty, sexual 13 Adolescentmaturation and driveFull physical growth, adult insociety, education complete,Young 21 beginning career, financialadultresponsibility, eligible forvotingRefinement of adult skills, 34 Mid adultparenting roleFulfillment of adult skills,serving, retirement begins with 55 Elder adulteligibility for Medicare, SocialSecurity 88. 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 89. , 90. PhiNo rational approximation for long e = 2.71828..... 2+ 5/7 7 arms = 3.141592 3 + 1/7 7 arms1+ 1 1+ 11+ 1 1+ 11+ 91. 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 - Russel Grigg 92. 2128 5 93. Da Vinci Code 94. amarnath.1960@gmail.com