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Golden Section and Fibonacci Numbers

Golden Section and Fibonacci Numbers. Optimum Design AME 60661,Spring 2009. Golden ratio. ( a+b )/a = a/ b = f 1 + 1/ f = f f ^2 – f – 1 = 0 f = (1+sqrt(5))/2 = 1.618033988749895 F = 1/ f = 0.6180339887. a = Top-of-head to chin

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Golden Section and Fibonacci Numbers

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  1. Golden Section and Fibonacci Numbers Optimum Design AME 60661,Spring 2009

  2. Golden ratio • (a+b)/a = a/b = f • 1 + 1/f = f • f^2 – f – 1 = 0 • f = (1+sqrt(5))/2 • = 1.618033988749895 • F = 1/f = 0.6180339887

  3. a = Top-of-head to chin b = Top-of-head to pupil c = Pupil to nosetip d = Pupil to lip e = Width of nose f = Outside distance between eyes g = Width of head h = Hairline to pupil i = Nosetip to chin j = Lips to chin k = Length of lips I = Nosetip to lips

  4. A B D C AB = 1, then AC = f, and AD = 1/f

  5. DC/BC = DE/CD = f

  6. Fibonacci Numbers 1 1 2 3 5 8 13 21

  7. 1

  8. 2

  9. 3

  10. 5

  11. 8

  12. 13

  13. 21

  14. 34

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