On Irrational Points in the Plane  

作　　者：Thomas Beatty Timothy Jones 

机构地区：[1]Florida Gulf Coast University, Fort Myers, Florida, USA

出　　处：《Advances in Pure Mathematics》2017年第4期299-305,共7页理论数学进展（英文）

摘　　要：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).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).

关 键 词：RATIONAL Point IRRATIONALITY SUM of Derivatives PRIME DIVISIBILITY HURWITZ Polynomial 

分 类 号：O1[理学—数学]