Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. ... However, although there is no way to trisect an angle in general with just a compass and a straightedge, some special angles can be trisected.

Why can't we Trisect an angle?

Since the roots have to add up to zero, this means that: ... Since the trisection equation has no constructible roots, and since cos(20°) is a root of the trisection equation, it follows that cos(20°) is not a constructible number, so trisecting a 60° angle by compass and straightedge is impossible.

Is it possible to Trisect a line segment?

A segment can be trisected in many ways. Most of the methods use similar triangles in some way. Below, two different ones are found. The first is a traditional trisecting of a segment.