**Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…**

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* *φ* if

**(a+b)/a = a/b = ****φ**

One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ:

**(a+b)/a =** **1+ b/a = 1+1/***φ*

Therefore: **1+1/***φ = **φ *

Multiplying by *φ* gives: *φ^2 - **φ - 1 = 0*

*Using the *quadratic formula*, two solutions are obtained:: *

**φ**** = (1- sqrt(5))/2 or ***φ* = (1+sqrt(5))/2

Because *φ* is the ratio between positive quantities *φ* is necessarily positive:

*φ *= (1+sqrt(5))/2 = 1.6180339887498948482…

See more at Golden Ratio.

Image: Phi (golden number) by Steve Lewis.