To construct [math]\Phi[/math] you start with a rectangular triangle with sides 1 and [math]\frac{1}{2}[/math].[list][*]Divide a square into two parts.[/*][*]Construct in one of the parts the diagonal and create a rectangular triangle with sides 1 and [math]\frac{1}{2}[/math].[/*][*]The length of the diagonaal 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 get [math]\Phi[/math] you have to add [math]\frac{1}{2}[/math].[br]You can do this by rotating the diagonal.[/*][/list]This construction is often used to construct a [i]golden rectangle[/i]. [br][list][*]The ratio between the long side and the short side is [math]\Phi[/math] =[math]\frac{\sqrt{5}+1}{2}[/math][/*][*]The ratio betwee the shortside and the long side is [math]\varphi[/math] = [math]\frac{\sqrt{5}-1}{2}[/math].[/*][/list]