Compass and Straightedge Constructions - Constructing Regular Polygons

Constructing Regular Polygons

Some regular polygons (e.g. a pentagon) are easy to construct with straightedge and compass; others are not. This led to the question: Is it possible to construct all regular polygons with straightedge and compass?

Carl Friedrich Gauss in 1796 showed that a regular n-sided polygon can be constructed with straightedge and compass if the odd prime factors of n are distinct Fermat primes. Gauss conjectured that this condition was also necessary, but he offered no proof of this fact, which was provided by Pierre Wantzel in 1837.

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