# 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} }

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

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

- Mathematics
- 2020

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 $\sqrt{2}$

- Mathematics
- 2009

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.

- Mathematics, Physics
- 2020

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

## References

SHOWING 1-7 OF 7 REFERENCES

### Three Proofs that the Square Root of 2 Is Irrational

- Computer Science

Three proofs that the square root of 2 is irrational are given and the first proof is a simple proof by contradiction and the second and third proofs use field theory from abstract algebra.

### “ ORIGAMI ” PROOFS OF IRRATIONALITY OF SQUARE ROOTS

- Mathematics
- 2008

If somehow you have not yet seen that proof, please ask someone, for example me, to show it to you. (Or maybe look at [2]. Well, meanwhile you can also extract it as a special case (substitute a = b…

### An Introduction to the Theory of Numbers

- MathematicsNature
- 1946

THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.…

### Basic Calculus: From Archimedes to Newton to its Role in Science

- Physics, Mathematics
- 1998

Part 1: From Archimedes to Newton * The Greeks Measure the Universe * Ptolemy and the dynamics of the universe * Archimedes measures area * A New Astronomy and a New Geometry * The Calculus of…

### Book of numbers

- PsychologyNature
- 1996

How Many People Can the Earth Support?By Joel E. Cohen. Norton: 1995. Pp. 532. $30, £22.50. UK publication date, 27 March.

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

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