### How to draw a regular pentagon with just ruler and compass?

### How about a regular hexagon?

__Underlying theorem:__Primes of the form 2

^{2n}+ 1 are known as Fermat primes.

A regular n-gon is constructible using straightedge (ruler) and compass if and only if

**n = 2**where

^{i}· m**m**is a product of any number of distinct Fermat Prime and

**i**is any natural number, including zero.

Only five Fermat primes are known: 3, 5, 17, 257, and 65,537.

Related study: Compass and straightedge constructions.

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