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.

M x

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