Trisecting an Angle—Almost

Abstract

Trisecting an angle with Euclidean tools, a straightedge and compass, has been proved to be impossible. However, many people today are still fascinated by the problem, and some even try to do it in spite of the proof to the contrary. The National Council of Teachers of Mathematics published a book on the subject titled The Trisection Problem (Yates 1971) that contains several methods proposed over the years. One method in particular, given by d'Ocagne, is easy and produces an angle that looks very close to the correct size, so close that only a proof that it fails will convince stubborn believers. The proof presented here uses only algebra and trigonometry and hopefully will show students how the three areas of algebra, trigonometry, and geometry can be interrelated.