Department of Mathematics
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The Pythagorean Theorem has been studied for well over 4000 years, has universal appeal, it is one of the most frequently used theorems in mathematics and several hundred proofs exist. Given such a glorious background, can one say anything new about this theorem? Recently there have been new proofs of Pythagorean theorem using ideas from analysis, mainly functional equations (also known as hyper-identities in Universal Algebra). In this talk, we show how functional equations occur naturally in the context of Pythagorean theorem and how the well-known solutions of these equations lead to a proof of this classical theorem of elementary geometry. Here we will witness a unique blend of analysis, algebra and geometry.

1. J. Aczel, Lectures on Functional Equations and their applications, Academic Press, New York, 1968.
2. L. Berrone, The associativity of the Pythagorean Law, AMS Monthly, 116 (2010), 936-939
3. E. Maor, The Pythagorean theorem: A 4,000-year history. Princeton Science Library. Princeton University Press, Princeton, NJ, 2008.