# Golden ratio

This calculator determines proportions according to golden ratio

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Created: 2011-06-19 22:06:58, Last updated: 2021-02-26 14:07:43

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This calculator determines proportions according to golden ratio. You can read about the golden ratio below the calculator

#### Golden ratio

Digits after the decimal point: 8
Long

Short

Sum

Golden ratio

Golden ratio also known as the divine proportion, golden mean, or golden section is a term for dividing a segment so the long/short ratio is equal to all/long ratio.
$\frac{a}{b}=\frac{a+b}{a}$
This number is constant.
If we suppose that b is 1, a should be equal to golden ratio. Let's substitute it for x
$\frac{x}{1}=\frac{x+1}{x}$
$x=\frac{x+1}{x}$
$x^2=x+1$
$x^2-x-1=0$

This is square equation. The positive root of the equation is
$\frac{1+\sqrt{5}}{2}$
and it is a golden ratio number
$\frac{\sqrt{5}+1}{2}=1,6180339887...$
It is irrational number.

The rough approximation of the golden ratio is the long part is 0,62 of all, and the short part is 0,38.

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PLANETCALC, Golden ratio