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.)
“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
The Kaplans (The Nothing That Is: A Natural History of Zero) have brought to life the Pythagorean theorem. They trace the development and treatment of this fundamental geometrical relationship from ancient times through the Middle Ages to the modern era. It is not an exaggeration to say that the Pythagorean theorem forms the basis of most of the mathematical expressions of our physical world. It is rare that a mathematical topic is presented in a manner that is light and entertaining and yet has depth and richness. The book is chock-full of geometrical illustrations along with ample equations and a few portrait images to accompany the abundant biographical information on mathematicians' whose proofs they consider. VERDICT Readers with some mathematical background will appreciate the geometrical and logical nuances, but even those less proficient in mathematics will grasp the essentials. Folks who love and live mathematics (and those in science and technology) will thoroughly enjoy this book. The Kaplans have given us a wonderful, fun, and entertaining math book.—Margaret Dominy, Drexel Univ. Lib., Philadelphia
Popular math writers Robert and Ellen Kaplan (Out of the Labyrinth: Setting Mathematics Free, 2007, etc.) examine the far-reaching, and at times exotic,applications ofthe familiar theorem.
With its origin traced back as far as ancient Babylon, the properties inherent in the Pythagorean Theorem (Asquared + B squared = Csquared) have had myriad implications both pedestrian and profound, from basic land-area assessment to architecture to physics. Thousands of people have worked out Pythagorean proofs, including President James Garfield while he was in the House of Representatives—further testament to both its alluringnature and astonishing versatility. (Interestingly, Pythagoras is not believed to have formulated the theorem named after him, which only adds to the mystique.) From a modern perspective, everything from differential calculus to astronomy utilizes the theorem's principles, and it has even been proven to apply to figures inmultiple dimensions,up to infinity, and to hint at the intriguing realm of irrational numbers.The authors, whose enthusiasm and wit make the material appealing even to readers who aren't mathematicians, write that such inspired deductions provide "the giddy sort of sensation that often leads people into mathematics: grasping something infinite via abstraction (as children love dinosaurs, because they are both very big and not quite real)." The book contains a healthy number of equations and proofs, some of which are intimidating, but the authors maintain an engaging plainspoken narrative peppered with references to, among many others, Shakespeare, Jefferson, Freud, Einstein andDescartes. It's clear that this theorem continues to play an important role in math and science, that the human capacity for theoretical exploration remains unabated and that our "curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity." As such, this engaginghistory ofthe elegantly simple theorem provides readers with much more to ponder than just the mathematical.
May not be widely accessible, but for the right reader, anenthralling exploration of this ancient rule of ratios.