GOLDEN RATIO

A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similargolden rectangle with longer side a + band shorter side a. This illustrates the relationship 

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. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,

${\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\ {\stackrel {\text{def}}{=}}\ \varphi ,}$

where the Greek letter phi (${\displaystyle \varphi }$ or ${\displaystyle \phi }$) represents the golden ratio. Its value is:

${\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.6180339887\ldots .}$  A001622

https://en.wikipedia.org/wiki/Golden_ratio