A '''regular polygon''' is a [[polygon]] where all the [[side]]s and included [[angle]]s are [[equal]]. Examples include the [[equilateral triangle]] and the [[square]].
The problem of which regular polygons can be constructed by ruler and compass alone goes back to the ancient Greeks. Some regular polygons (e.g. a regular pentagon) can be constructed with a straightedge (without any markings) and compass, others cannot. Carl Friedrich Gauss 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 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>.
The construction of the regular 17-sided polygon is an inscription on Gauss' tomb.