Constructing a Regular Heptadecagon (17-gon) with Ruler and Compass
The number 17 is a Fermat prime, which means it is of the form , with . In 1796, Gauss discovered that regular polygons with a Fermat number of sides can be constructed using only a straight edge and compass . Gauss showed, in particular, that
This is derived in [1, 2]. An explicit construction of a regular heptadecagon was given by H. W. Richmond in 1893 . This Demonstration is based on his method. A reproduction of Richmond's paper is shown in the Details. Alternative constructions have since been proposed (see, for example, the MathWorld article).