Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, ..., sides. In 1796 (when he was 19 years old), Gauss gave a sufficient condition for a regular n-gon to be constructible, which he also conjectured (but did not prove) to be necessary, thus showing that regular n-gons were constructible for n = 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, ... (OEIS A003401). A complete enumeration of "constructible" polygons is given by those with central angles corresponding to so-called trigonometry angles.

compass | constructible number | cyclotomic polynomial | Fermat number | geometric construction | geometrography | heptadecagon | hexagon | octagon | pentagon | polygon | Sierpiński sieve | square | straightedge | triangle | trigonometry angles