Golden Ratio

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

Also related to how $\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{\frac{1}{x+1}+1}+1}+1}+1}+1}+1}+1}+1}+1}$ is approximately $\frac{\sqrt{5}-1}{2}$ for any $x$