Synopses & Reviews
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.
Review
The Kaplans (Out of the Labyrinth) collaborate for a fourth time on this historical and mathematical examination of the Pythagorean Theorem (a2+b2=c2). 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. Some readers may wish for a more direct approach but the Kaplans combine math history and theory with humor compelling tidbits and helpful equations (along with an analysis of tangrams) to create an entertaining and stimulating book for the mathematically inclined. Illus. (Jan.) " Publishers Weekly Copyright PWxyz, LLC. All rights reserved."
Review
"The Kaplans (Out of the Labyrinth) collaborate for a fourth time on this historical and mathematical examination of the Pythagorean Theorem (a2+b2=c2). 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. Some readers may wish for a more direct approach, but the Kaplans combine math history and theory with humor, compelling tidbits, and helpful equations (along with an analysis of tangrams) to create an entertaining and stimulating book for the mathematically inclined. Illus. (Jan.)" Publishers Weekly (Copyright PWyxz LLC)
Review
“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. Marks 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 theorems 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 its often as fun to be around…”—Anthony Doerr, Boston Globe
“The Kaplans have given us a wonderful, fun, and entertaining math book.”—Library Journal
Synopsis
With wit, verve, and clarity, the authors trace the life of the Pythagorean theorem, from ancient Babylon to the present.
Synopsis
A squared plus b squared equals c squared. It sounds simple, doesnt it? Yet this familiar expression opens a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, 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. As in the authors bestselling The Nothing That Is and Chances Are..., the excitement of mathematics leaps from the pages of Hidden Harmonies.
About the Author
Robert and Ellen Kaplan have taught mathematics to people from six to sixty, at leading independent schools and, most recently, at Harvard University. Robert Kaplan is the author of the bestselling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages, and together they wrote The Art of the Infinite and Out of the Labyrinth. 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. They live in Southampton, Massachusetts.