Author(s)

Thomas Beatty, Timothy Jones

Florida Gulf Coast University, Fort Myers, Florida, USA.

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)∈R² 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).

Rational Point, Irrationality, Sum of Derivatives, Prime, Divisibility, Hurwitz Polynomial

Beatty, T. and Jones, T. (2017) On Irrational Points in the Plane. Advances in Pure Mathematics, 7, 299-305. doi: 10.4236/apm.2017.74016.