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 $1.618$.