How to construct an n-gon by ruler and compass? Since $\cos[\frac{2\pi}{15}] $ is algebraic and equal to  $\frac{1}{8}(1+\sqrt{5}+\sqrt{30-6\sqrt{5}})$ we know that the regular 15-gon is constructible by ruler and compass.
Although I know how to construct a hexagon by ruler and compass and have seen the construction of a pentagon done in a youtube video, I can't find a description of a general approach to constructing n-gons where $n>7$ anywhere.
Is there a general approach, geometric algorithm if you like, to constructing an n-gon by ruler and compass?

If you can read French (purely mathematical), you'll find on this page applets for the geometric construction of the pentagon, and the penta- & heptadecagons.
