Mechanism analysis of a trisector

This paper presents a graphical procedure for analyzing a trisector – a mechanism used for trisecting an arbitrary acute angle. The trisector employed was a working model designed and built for this purpose. The procedure, when applied to the mechanism at the 60° angle, which has been proven to be not trisectable as well as the 45° angle for benchmarking (since this angle is known to be trisectable), produced results that compared remarkably in both precision and accuracy. For example, in both cases, the trisection angles found were 20.00000°, and 15.00000°, respectively, as determined by The Geometer’s Sketch Pad software. Considering the degree of accuracy of these results (i.e. five decimal places) and the fact that it represents the highest level of precision attainable by the software, it is felt that the achievement is noteworthy, notwithstanding the theoretical proofs of Wantzel, Dudley, and others [Underwood Dudley, A Budget of Trisections, Springer-Verlag, New York, 1987; Clarence E. Hall, The equilateral triangle, Engineering Design Graphics Journal 57 (2) (1993); Howard Eves, An Introduction to The History of Mathematics, sixth ed., Saunders College Publishing, Fort Worth, 1990; Henrich Tietze, Famous Problems of Mathematics, Graylock Press, New York, 1965].