A possible solution of trisection problem

Abstract

A solution of the ancient Greek problem of trisection of an arbitrary angle employing only compass and straightedge and its algebraic proof are presented. It is shown that while Wantzel's [1] theory of 1837 concerning irreducibility of the cubic x3 - 3x - 1 = 0 is correct it does not imply impossibility of trisection of arbitrary angle since rather than a cubic equation the trisection problem is shown to depend on the quadratic equation y2 - 3 + c = 0 where c is a constant. The earlier formulation of the problem by Descartes the father of algebraic geometry is also discussed. If one assumes that the ruler and the compass employed in the geometric constructions are in fact Platonic ideal instruments then the trisection solution proposed herein should be exact.