Famous constant denoted by $\phi$.
$\huge \phi = \frac{1+\sqrt{ 5 }}{2} $
Which is the positive root of $x^2-x-1=0$.
Divide a segment into two pieces $a$ and $b$ where $a>b$.
The ratio $\frac{a}{b}$ is the golden ratio if $\frac{a}{b}=\frac{a+b}{a}$.
>[!tldr] Proof
>$
>\begin{align}
>\frac{x}{y} &= \frac{{x+y}}{x} \\
>
>x^2 &= y(x+y) \\
>x^2 &= xy+y^2 \\
>x^2-xy-y^2 &= 0\\
>x^2 - yx-y^2 &= 0\\
>
>x &= \frac{y \pm \sqrt{ y^2 - 4-y^2 }}{2}\\
>&= \frac{y \pm y \sqrt{ 5 }}{2} \\
>x \in \Z^{+} \implies
>x &= \frac{y + y \sqrt{ 5 }}{2} \\
>\\
>
>\phi &= \frac{x}{y} \\
>&=\frac{1 \pm \sqrt{ 5 }}{2} \\
>\end{align}
>$