[list][*]In a regular n-sided polygon with radius r the side z is calculated as [math]z=2r.sin\frac{\pi}{n}[/math] [/*][*]For a regular decagon with radius 1 you find: [math]z=2.sin\frac{\pi}{10}[/math][br][/*][*]The equality [math]sin\frac{\pi}{10}=\frac{\varphi}{2}[/math]implies: in a regular decagon with radius 1 the side is [math]z=\varphi=\frac{\sqrt{5}-1}{2}[/math].[/*][/list]In a unit circle one can draw a regular decagon: