Golden ratio

Definition

The golden ratio is the number:

${\frac {1+{\sqrt {5}}}{2}}$

It is the unique positive solution to any of these equations:

• $x^{2}=x+1$, i.e., $x^{2}-x-1=0$
• $x={\frac {1}{x}}+1$, i.e., $x-{\frac {1}{x}}-1=0$

The approximate value of the golden ratio is $1.618$.