TITLE:
On Irrational Points in the Plane
AUTHORS:
Thomas Beatty, Timothy Jones
KEYWORDS:
Rational Point, Irrationality, Sum of Derivatives, Prime, Divisibility, Hurwitz Polynomial
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.4,
April
20,
2017
ABSTRACT: This paper summarizes research intended to develop a pedagogically friendly
argument that establishes the fact that (x,ex ) 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).