A heptadecagon (or a 17-gon) is a seventeen sided polygon.
Constructing the Heptadecagon
In 1796, Gauss proved, at the age of 19 (let that sink in…) that the heptadecagon is constructible with a compass and a straightedge, such as a ruler. His proof of the constructibility of an n-gon relies on two things:
- the fact that “constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions“;
- the odd prime factors of n are distinct Fermat primes.
Constructing the regular heptadecagon involves finding the expression for the cosine of in terms of square roots, which Gauss gave in his book Disquistiones Arithmeticae:
An explicit construction was given by Herbert Willian Richmond in 1893.