Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…In mathematics, two quantities are in the

golden ratioif their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantitiesaandbwitha>b> 0. Two quantitiesaandbare said to be in thegolden ratioφif

(a+b)/a = a/b =φOne 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/φTherefore:

1+1/φ =φ

Multiplying byφgives:φ^2 -φ - 1 = 0

Using thequadratic formula, two solutions are obtained::

φ= (1- sqrt(5))/2 orφ= (1+sqrt(5))/2Because

φis the ratio between positive quantitiesφis necessarily positive:

φ= (1+sqrt(5))/2 = 1.6180339887498948482…See more at Golden Ratio.

Image: Phi (golden number) by Steve Lewis.

(via visualizingmath)

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