Golden Ratio Calculator

・Examples of the use of the golden ratio include the Parthenon as seen from the front, the base and height of the pyramids, and the painting *Mona Lisa*.
It appears to have been used since ancient times as a stable and beautiful ratio.

\(\normalsize Golden\ ratio\\ (1)\ a\ :\ b=a+b\ :\ a=\ {\large\frac{1+\sqrt{5}}{2}}\ :\ 1\\ (2)\ \phi={\large\frac{a}{b}}={\large\frac{a+b}{a}}=1.61803\cdots\\ (3)\ \phi=1+{\large\frac{1}{1+{\large\frac{1}{1+\cdots}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}\\\)