A UNIQUE METHOD FOR THE TRISECTION OF AN ARBITRARY ANGLE

Abstract

Trisection of an arbitrary angle is considered an impossible event in mathematical history. In this paper, we are trying to establish a general procedure for trisecting an arbitrary angle using only an unmarked straightedge and a compass. The basic geometrical compass constructions described in our main results section will ensure the possibilities of known and unknown angles trisection indeed. Before reaching the main results or general trisecting procedure, we will try to prove that Angles of sixty, thirty, seventy-five, forty-five, and ninety degrees can be trisected successfully by following the way of Archimedes and other discrete endeavors. Although based on algebra, Pierre Laurent Wantzel declared the verdict, “Arbitrary angle trisection is impossible.” we experienced that our achieved procedure was possibly not arrested by this verdict. After applying our general process to trisect an arbitrary angle, we hope readers can trust algebra cannot affect the successful geometrical constructions of angle trisection.