On Irrational Points in the Plane

Abstract

This paper summarizes research intended to develop a pedagogically friendly argument that establishes the fact that (x,e x ) is never a rational point in the plane. A point (x, y)∈R 2 is rational if both x and y are rational. Applying a method based on Hurwitz polynomials, the research establishes simple irrationality proofs for nonzero rational powers of e and logarithms of positive rationals (excluding one).