A Simplified Graphical Procedure for Constructing a 10˚ or 20˚ Angle
- 1 Delaware State University, Dover, USA
Abstract
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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