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# A Proof that π Is Irrational

by

Paul Friedman
Union College

January 10, 2011
4:30 pm
Bailey Hall 207

Refreshments will be served in Bailey 204 at 4:15 pm

## Abstract:

A rational number is a real number that can be written as the quotient of two integers. For example, 22/7 is rational. An irrational number is a real number that is not rational, that is, it cannot be written as the quotient of any two integers.

Famously, the ancient Greeks were able to prove that $\sqrt 2$ is irrational – perhaps you have seen a proof of this in Math 199. You have quite possibly been told that π is irrational. But have you ever seen a proof of this result?

The first proof of the irrationality of π is attributed to J. H. Lambert in 1761. Since then, many other proofs have been discovered, including a short (one-page) proof by I. Niven in 1947. In April 2010, Zhou and Markov published an even shorter (one paragraph!) proof, if some details are omitted. In this seminar talk, without omitting too many details, using some basic calculus, we will prove that π is irrational in the manner of Zhou and Markov.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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