Golden Section and Fibonacci Numbers

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

5. 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

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

9. DC/BC = DE/CD = f

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

12. 1

13. 2

14. 3

15. 5

16. 8

17. 13

18. 21

19. 34