TITLE:
A Procedure for Trisecting an Acute Angle
AUTHORS:
Lyndon O. Barton
KEYWORDS:
Archimedes’ Construction, College Geometry, Angle Trisection, Trisectors, Famous Problems in Mathematics, History of Mathematics
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.2,
February
14,
2022
ABSTRACT: This paper presents a graphical procedure, using an unmarked straightedge and compass only, for trisecting an arbitrary acute angle. The procedure, when applied to the 30˚ angle that has been “proven” to be not trisectable, produced a construction having the identical angular relationship with Archimedes’ Construction, in which the required trisection angle was found to be exactly one-third of the given angle (or ∠E'MA = 1/3∠E'CG = 10˚), as shown in Figure 1(D) and Figure 1(E) and Section 4 PROOF in this paper. Hence, based on this identical angular relationship between the construction presented and Archimedes’ Construction, one can only conclude that geometric requirements for arriving at an exact trisection have been met, notwithstanding the theoretical proofs of Wantzel, Dudley, and others.