Let's Teach Angle Trisection

Abstract

Every Year several people announce that they have discovered a method for trisecting angles in the belief that they have solved the classical trisection problem. Many of the methods discovered are correct in the sense that they may be used to trisect an arbitrary angle; many of the methods have been discovered so frequently that they are practically classics themselves. The part of the problem that these discoverers apparently do not understand is that the classical problem requires that the trisection be done using only compasses and a straightedge. The straightedge may be used only to draw straight lines. In solving the classical construction problems one is not allowed to use the length or width of the straightedge, and similarly one is not allowed to use marks upon it. When these classical restrictions upon the trisection problem are disregarded, many of the constructions for the trisection of angles can be performed using only the methods now taught in secondary schools. The restriction that there should be no marks upon the straightedge is disregarded in one of the simplest and oldest constructions of the trisection of angles. This construction is attributed to Archimedes. It requires only compasses and a straightedge with two marks on it. A ruler will serve very well.