Trisecting an angle is one of the three classical problems of Greek geometry, together with doubling the cube and squaring the circle. Although it is one of the oldest problems of mathematics, it is also one of the most misunderstood. The problem of trisecting an angle has been proven to be impossible, but mathematicians daily receive "proofs" from amateur mathematicians who believe they have found a way to trisect the angle.

The original problem considered by Greek mathematicians was to find a way to trisect any given angle using only "plane" methods, that is, using only two pieces of equipment: a compass and an unmarked straightedge. Most of the people who believe they have found a way to trisect the angle have inadvertently used the straightedge for measuring; often their error is buried so deep that it is difficult to detect.

It is important...