Number Theory


The Irrationality of Trigonometric and Hyperbolic Functions

Authors: Timothy W. Jones

This article simplifies Niven's proofs that cos and cosh are irrational when evaluated at non-zero rational numbers. Only derivatives of polynomials are used. This is the third article in a series of articles that explores a unified approach to classic irrationality and transcendence proofs.

Comments: 7 Pages. This version adds an example using Leibniz tables.

Download: PDF

Submission history

[v1] 2017-11-12 10:24:36
[v2] 2017-11-14 09:52:19
[v3] 2017-11-16 09:44:04
[v4] 2017-11-30 10:59:47

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