Hidden Harmonies

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.