Hidden Harmonies: The Lives and Times of the Pythagorean Theorem

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.)