/* Construction of Regular Polygons */

===Construction of Regular Polygons===

The problem of which regular polygons can be constructed by ruler and compass alone goes back to the [[Ancient Greece|ancient Greeks]]. Some regular polygons (e.g. a regular [[pentagon]]) can be constructed with a straightedge (without any markings) and compass, others cannot. [[Gauss| Carl Friedrich Gauss]] made the first new progress on the problem when he constructed the regular 17-gon in 1796. He later showed that a regular n-sided polygon can be constructed with ruler and compass if the odd prime factors of n are distinct [[Pierre de Fermat|Fermat]] primes <ref>This result is recorded in Section VII of Gauss's Disquisitiones Arithemeticae published in 1801. Gauss conjectured that this condition was also necessary, but he offered no proof of this fact, which was proved by Pierre Wantzel in 1837 </ref>.