• Corpus ID: 115166938

# Irrationality From The Book

@article{Miller2009IrrationalityFT,
title={Irrationality From The Book},
author={Steven J. Miller and David Montague},
journal={arXiv: History and Overview},
year={2009}
}
• Published 27 September 2009
• Mathematics
• arXiv: History and Overview
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.
3 Citations

## Figures from this paper

### A geometric proof that $\sqrt{n}$ is irrational for $n$ not a square

For any positive integer $n$ which is not a square we show geometrically that $\sqrt n$ is irrational by generalizing Tennenbaum's geometric proof that $\sqrt 2$ is irrational.

### Real numbers as infinite decimals and irrationality of $\sqrt{2}$

In order to prove irrationality of \sqrt{2} by using only decimal expansions (and not fractions), we develop in detail a model of real numbers based on infinite decimals and arithmetic operations

### A geometric proof that $\sqrt{3}$, $\sqrt{5}$ and $\sqrt{7}$ are irrational.

We show geometrically that $\sqrt n$ is irrational for $n=3,5,7$ by adapting Tennenbaum's geometric proof that $\sqrt 2$ is irrational.

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### E-mail address: davmont@umich.edu DEPARTMENT OF MATHEMATICS

• E-mail address: davmont@umich.edu DEPARTMENT OF MATHEMATICS