homechevron_rightStudychevron_rightMath

# Golden ratio

This calculator determines proportions according to golden ratio

This calculator determines proportions according to golden ratio. You can read about golden ration 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 golden ratio is the long part is 0,62 of all, and short part is 0,38.

#### Similar calculators

PLANETCALC, Golden ratio