Constructibility of the Regular Heptadecagon

On 30 March 1796, a nineteen year old Carl Friedrich Gauss proved that a regular seventeen-sided polygon can be constructed using only a compass and an unmarked straightedge, the first advance on the classical problem of which regular polygons are so constructible since Euclid's own era. Gauss showed the seventeenth roots of unity could be expressed using only square roots (the operations a compass and straightedge can perform), a result he generalized to identify exactly which regular polygons are constructible: those with a prime number of sides that is a Fermat prime, or products and powers of such primes with a power of two. He considered the discovery important enough to request a regular seventeen-gon be engraved on his own gravestone, though the stonemason reportedly declined, believing it would be indistinguishable from a circle.