Thursday, December 10, 2009

Drawing Regular n-gon

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

How about a regular hexagon?

Underlying theorem:
Primes of the form 22n + 1 are known as Fermat primes.

A regular n-gon is constructible using straightedge (ruler) and compass if and only if n = 2i · m where 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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