Hidden Harmonies

Hidden Harmonies

The Lives and Times of the Pythagorean Theorem

By Ellen Kaplan; Robert Kaplan

Bloomsbury Publishing PLC, Hardcover, 9781596915220, 304pp.

Publication Date: January 4, 2011


"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.

About the Author
Ellen Kaplan has taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. With her husband, Robert, she wrote The Art of the Infinite. Ellen is also co-author of Chances Are: Adventures in Probability and Bozo Sapiens: Why to Err is Human, co-written with her son, Michael Kaplan.

Praise For Hidden Harmonies

“Beauty, intrigue, paradox and surprise. Mathematics, in its true essence, is a deeply organic and intensely human enterprise and Bob and Ellen Kaplan are the masters of reveling in its delight and elucidating its richness. Hidden Harmonies is a stunning book, taking the most classic theorem in mathematics and exposing its story, its human story, for what it really is: true poetry.”—James Tanton, PhD, author and educator, founding director of the St. Mark’s Institute of Mathematics

“…The authors succeed in explaining the arcane aspects of the subject, and they are diligent in situating the Pythagorean theorem within the historical rise of mathematics. That they revel in the subject is clear…”Wall Street Journal


“Showing the theorem’s endless versatility, the Kaplans and their logic- and symbol-permeated text will engage those who delight in doing the math.”—Booklist


“Enthusiasm and wit make the material appealing even to readers who aren't mathematicians … inspired.”—Kirkus


“The book possesses an alluring lyricism and a good sense of humor, and it’s often as fun to be around…”—Anthony Doerr, Boston Globe


“The Kaplans have given us a wonderful, fun, and entertaining math book.”Library Journal