Trisecting an Angle—Almost, Part 2

Abstract

When students study constructions in high school geometry, they usually make the following conjecture: Since it is easy to bisect a line segment, easy to bisect an angle, and not too difficult to trisect a line segment, there ought to be a way to trisect an angle. The students may even devise ways that they think will accomplish the task. The errors in these methods are sometimes hard to detect. This article highlights one way that has been discovered that comes very close to trisecting an angle with Euclidean tools. Several ways are discussed in one of the books in the Classics in Mathematics Education series published by the National Council of Teachers of Mathematics titled The Trisection Problem (Yates 1971). One of the methods discovered by d'Ocagne was examined in “Trisecting an Angle—Almost” (Lamb 1988). His method was very easy to do, but it was not as accurate as some of the other methods. One of those methods that is also relatively easy to do and gives a much better approximation than the d'Ocagne method for angles between 0 degrees and 90 degrees was discovered by Karajordanoff in 1928 (Yates 1971). The procedure is as follows.