A Simplified Graphical Procedure for Constructing a 10˚or 20˚Angle
A Simplified Graphical Procedure for Constructing a 10˚or 20˚Angle作者机构：Delaware State University Dover USA
出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)
年 卷 期：2023年第13卷第7期
页 面：442-448页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Archimedes’ Construction College Geometry Angle Trisection Trisection of an Angle Famous Problems in Mathematics. Geometer’s Sketch Pad Mechanisms Mechanism Analysis Kinematics Trisector
摘 要：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.
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