The important result is the Gauss-Wantzel theorem:
A regular n-gon is constructible with ruler and compass if and only if n = 2k (k ≥ 2) or if n = 2kp1p2...pt where k is a non-negative integer, t is a positive integer, and each pi is a (distinct) Fermat prime.
Comments
The important result is the Gauss-Wantzel theorem:
A regular n-gon is constructible with ruler and compass if and only if n = 2k (k ≥ 2) or if n = 2kp1p2...pt where k is a non-negative integer, t is a positive integer, and each pi is a (distinct) Fermat prime.
If you want to dig deeper, start with http://en.wikipedia.org/wiki/Constructible_polygon
or
http://planetmath.org/encyclopedia/CriterionForCon... which gives a short proof of the theorem.
SOME n-gons ARE constructible. some aren't. it depends on n.