Hidden Harmonies: The Lives and Times of the Pythagorean Theorem

A squared plus b squared equals c squared. It

sounds simple, doesn't it? Yet this familiar expression is a gateway

into the riotous garden of mathematics, and sends us on a journey of

exploration in the company of two inspired guides, acclaimed authors

Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the

life of the Pythagorean theorem, from ancient Babylon to the present,

visiting along the way Leonardo da Vinci, Albert Einstein, President

James Garfield, and the Freemasons-not to mention the elusive Pythagoras

himself, who almost certainly did not make the statement that bears his

name.

How can a theorem have more than one proof? Why does this one have

more than two hundred-or is it four thousand? The Pythagorean theorem

has even more applications than proofs: Ancient Egyptians used it for

surveying property lines, and today astronomers call on it to measure

the distance between stars. Its generalizations are stunning-the theorem

works even with shapes on the sides that aren't squares, and not just

in two dimensions, but any number you like, up to infinity. And perhaps

its most intriguing feature of all, this tidy expression opened the door

to the world of irrational numbers, an untidy discovery that deeply

troubled Pythagoras's disciples.

Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"-Hidden Harmonies makes the excitement of mathematics palpable.

© 2011 Bloomsbury Press (E-bog): 9781608192915

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E-bog: 11. januar 2011