Golden Ratio Ï† = (1+sqrt(5))/2 = 1.6180339887498948482â€¦
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Two quantities a and b are said to be in the golden ratio Ï† if
(a+b)/a = a/b = Ï†
One method for finding the value of Ï† is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/Ï†:
(a+b)/a = 1+ b/a = 1+1/Ï†
Therefore: 1+1/Ï† = Ï†
Multiplying by Ï† gives: Ï†^2 – Ï† – 1 = 0
Using the quadratic formula, two solutions are obtained::
Ï† = (1- sqrt(5))/2 or Ï† = (1+sqrt(5))/2
Because Ï† is the ratio between positive quantities Ï† is necessarily positive:
Ï† = (1+sqrt(5))/2 = 1.6180339887498948482â€¦
See more at Golden Ratio.
Image: Phi (golden number) by Steve Lewis.
From Ratak Monodosico.