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A Simplified Graphical Procedure for Constructing a 10˚or 20˚Angle

Advances in Pure Mathematics 2023年第7期13卷 442-448页

作者： Lyndon O. Barton Delaware State University Dover USA

This paper presents a simplified graphical procedure for constructing, using an unmarked straightedge and a compass only, a 10˚ to 20˚ angle, which is in other words, trisecting a 30˚ or 60˚ angle. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angles were found to be 10.00000˚ and 20.00000˚ respectively (i.e. exactly one-third of the given angle or ∠E’MA = 1/3∠E’CG). Based on this identical angular relationship as well as the numerical results obtained, one can only conclude that the geometric requirements for arriving at an exact trisection of the 30˚ or 60˚ angle, and therefore the construction of a 10˚ or 20˚ angle, have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others. Thus, the solution to the age-old trisection problem, with respect to these two angles, has been accomplished.

关键词： Archimedes’ Construction College Geometry Angle Trisection Trisection of an Angle Famous Problems in Mathematics. Geometer’s Sketch Pad Mechanisms Mechanism Analysis Kinematics trisector

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A Key to Solving the Angle Trisection Problem

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Advances in Pure Mathematics 2023年第9期13卷 625-634页

作者： Lyndon O. Barton Department of Math and Physics Delaware State University Dover USA

This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” 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 results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.

关键词： Archimedes’ Construction College Geometry College Mathematics Angle Trisection trisector Famous Problems in Mathematics History of Mathematics Mechanism Analysis Kinematics Geometer’s Sketch Pad

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