Compass and Straightedge Construction for Regular Heptagon does not exist/Proof 1

Theorem

There exists no compass and straightedge construction for the regular heptagon.

Proof

By definition, the regular heptagon has $7$ sides.

$7$ is a prime number which is not a fermat prime.

The result follows Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime.

$\blacksquare$

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)