To construct [math]\varphi[/math] you start with a rectangular triangle with sides 1 and [math]\frac{1}{2}[/math].[br][list][*]Divide the square into two parts.[/*][*]Construct in in one of them the diagonal to create a rectangular triangle with sides 1 and [math]\frac{1}{2}[/math].[/*][*]The length of the diagonal becomes [math]\sqrt{1+\left(\frac{1}{2}\right)^2}=\sqrt{1+\frac{1}{4}}=\sqrt{\frac{5}{4}}=\frac{\sqrt{5}}{2}[/math].[br][/*][*]To become [math]\varphi[/math] you have to substract [math]\frac{1}{2}[/math] of it.[br]To do this you can draw a circular arc with radius [math]\frac{1}{2}[/math] on the diagonal.[/*][/list]