Hidden Harmonies

With wit, verve, and clarity, Robert Kaplan and Ellen Kaplan 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.

 

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

Praise

“…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…”—The Wall Street Journal

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

“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

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

“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

"Going well beyond the typical school treatment of the subject, the Kaplans use proofs and diagrams to demonstrate that 'the Pythagorean Theorem . . . holds even when the most art nouveau shapes flourish on a right triangle's hypotenuse, along with shapes similar to it on the legs. They can, if you wish, be as lacy as your great-grandmother's antimacassars, so long as they have areas.' People throughout the ages, from Leonardo da Vinci to President James A. Garfield, have found multiple methods for constructing proofs of this famous and useful theorem, and the Kaplans provide many of them along with background information and context. The Kaplans are wonderfully chatty hosts—'The begottens and begets of mathematics never end—not because of some dry combinatorial play, but because curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity'—often asking questions to inspire thinking."—Publishers Weekly

About the Author(s)

By Robert Kaplan and Ellen Kaplan

Robert Kaplan is the author of the best-selling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages. 

 

Ellen Kaplan 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.

 

Together they wrote The Art of the Infinite.