Gauss showed in 1796 that a regular 17-gon can be constructed by using a compass and a straightedge ruler, since [math]\cos\frac{2\pi}{17}=\frac{\sqrt17+\sqrt{34-2\sqrt17}+2\sqrt{17+3\sqrt17-\sqrt{34-2\sqrt17}-2\sqrt{34+2\sqrt17}}-1}{16}[/math].[br]Here we follow H. W. Richmond's step by step [url=https://en.wikipedia.org/wiki/Heptadecagon]recipe[/url] to construct the regular 17-gon.