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A serendipitous path to a famous inequality

Published online by Cambridge University Press:  01 August 2016

Robert M. Young
Robert M. Young*
Affiliation:
Department of Mathematics, Oberlin College, Oberlin, OH 44074 USA, e-mail: robert.young@oberlin.edu
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Extract

The mysterious path of discovery – the tireless experimentation in search of patterns, the veiled connections that suddenly unfold, serendipity – all these elements combine to make mathematics so magical. The purpose of this note is to show how a routine algebraic identity, the binomial expansion of (x - 1)2, can be used to give a new proof of the fundamental inequality between the arithmetic and geometric means. The proof will provide further evidence that a great deal of useful mathematics can be derived from the obvious assertion that the square of a real number is never negative.

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Articles
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The Mathematical Gazette , Volume 92 , Issue 523 , March 2008, pp. 50 - 54
Copyright
Copyright © The Mathematical Association 2008

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