Kinematics: A Key to Solving the Angle Trisection Problem - Lyndon O. Barton (Mathematics and Computer Science: Contemporary Developments Vol. 10, 2024)
This paper is a sequel to its forerunner entitled, “A Procedure for Trisecting an Acute Angle,” published earlier where it presented a construction capable of dividing any arbitrary acute angle into three exactly equal parts using an unmarked straightedge and compass only. This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem. It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics, to arrive at the desired construction, using an unmarked straightedge and a compass only. In presenting this construction, since there was no requirement to provide a detailed logic behind the procedure, this information was not provided. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis, in graphical detail, that formed the basis of the long-sought solution to the age-old Angle Trisection Problem, that goes back to the period of Archemedes (around 250 B.C.). The study concluded that this long-sought solution has been finally accomplished, notwithstanding the theoretical proofs of Wantzel, Dudley, and others.