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A squared plus b squared equals c squared. It sounds simple, doesn’t 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 ...
A squared plus b squared equals c squared. It sounds simple, doesn’t 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.
“…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
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.
An Outlook on Insights xi
Chapter 1 The Mathematician as Demigod 1
Chapter 2 Desert Virtuosi 6
Chapter 3 Through the Veil 44
Chapter 4 Rebuilding the Cosmos 63
Chapter 5 Touching the Bronze Sky 81
Chapter 6 Exuberant Life 138
Chapter 7 Number Emerges from Shape 177
Chapter 8 Living at the Limit 192
Chapter 9 The Deep Point of the Dream 224
Chapter 10 Magic Casements 254
Afterword Reaching Ihrough-or Past-History? 262
Selected Bibliography 277
Posted September 24, 2011
For anyone interested in Mathematics, at sny level, the Pythagorian Theorem is ubiquitous, to say the least. I was surprised to learn that Pythagoras was a Johnny-come-lately in the right triangle game. I was also surprised at the story of a Cleveland Geometry teacher who devised about 300 different proofs for the Theorem. He taught at a Cleveland high school at the turn of the century. Now, a century later, I'm teaching Geometry at the same school. The book is loaded with surprises. By all means - read it
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Posted May 23, 2011