Editing Angle trisection (section)

==Background and problem statement==
[[Image:Bisection construction.gif|thumb|[[Bisection]] of [[arbitrary]] [[angle]]s has long been solved.]]
Using only an unmarked [[straightedge]] and a compass, [[Greek mathematics|Greek mathematicians]] found means to divide a [[Line (mathematics)|line]] into an arbitrary set of equal segments, to draw [[Parallel (geometry)|parallel]] lines, to [[Bisection#Angle bisector|bisect angle]]s, to construct many [[polygon]]s, and to construct [[Square (geometry)|square]]s of equal or twice the area of a given polygon.

Three problems proved elusive, specifically, trisecting the angle, [[doubling the cube]], and [[squaring the circle]]. The problem of angle trisection reads:

Construct an [[angle]] equal to one-third of a given arbitrary angle (or divide it into three equal angles), using only two tools:
# an unmarked straightedge, and
# a compass.