Irrationality From The Book

TL;DR

This paper extends Tennenbaum's geometric proof of the irrationality of sqrt(2) to other non-square integers such as 3, 5, 6, and 10, providing a broader geometric perspective on irrationality.

Contribution

It generalizes a classical geometric proof to multiple non-square integers, enhancing understanding of irrationality proofs.

Findings

Geometric proof applicable to sqrt(3), sqrt(5), sqrt(6), and sqrt(10)

Provides a unified geometric approach to irrationality

Published in Mathematics Magazine, 2012

Abstract

We generalize Tennenbaum's geometric proof of the irrationality of sqrt(2) to sqrt(n) for n = 3, 5, 6 and 10. Modified version published in Mathematics Magazine \textbf{85} (2012), no. 2, 110--114.