Golden Section and Fibonacci Numbers

Optimum Design

AME 60661,Spring 2009

(a+b)/a = a/b = f

1 + 1/f = f

f^2 – f – 1 = 0

f = (1+sqrt(5))/2

f = 1.618033988749895

F = 1/ = f 0.6180339887

Golden ratio

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

A

B

AB = 1, then AC = f, and AD = 1/f

C

D

DC/BC = DE/CD = f

Fibonacci Numbers1

1

2

3

5

8

13

21

1

2

3

5

8

13

21

34