The Pythagorean Theorem: A 4,000-Year History »

Eli Maor teaches the history of mathematics at Loyola University in Chicago. He is the author of "Venus in Transit, Trigonometric Delights, e: The Story of a Number", and "To Infinity and Beyond: A Cultural History of the Infinite" (all Princeton).

"At last, a popular book that isn't afraid to print a mathematical formula in all its symbolic glory! Thanks to Eli Maor for proving—in his delightful, playful way—the eternal importance of a three-sided idea as old as humankind."—Dava Sobel, author of Longitude

"Eli Maor has brought four thousand years of history back to life, all based on the Pythagorean theorem but still giving the times a distinctly human look. This book is designed for readers who are inspired, or who want to be inspired, by the numbers that Eli uses to tell his story. Readers will learn about the mathematics of the time, but more important, they will understand the people and the ideas of that period. A monumental effort."—David H. Levy, National Sharing the Sky Foundation

"There's a lot more to the Pythagorean theorem than a² + b² = c², and you'll find it all in Eli Maor's new book. Destined to become a classic, this book is written with Maor's usual high level of skill, scholarship, and attention to detail. He's also got a sense of humor that will please a range of readers. As we used to say in the 1950s, 'Miss it and be square!'"—Paul J. Nahin, author of Chases and Escapes and Dr. Euler's Fabulous Formula

"Eli Maor states that the Pythagorean theorem 'is arguably the most frequently used theorem in all of mathematics.' He then supports this claim by taking his reader on a journey from the earliest evidence of knowledge of the theorem to Einstein's theory of relativity and Wiles's proof of Fermat's last theorem, from the Babylonians around 1800 BCE to the end of the twentieth century. I think that the reader who makes the journey with Maor will be convinced beyond a reasonable doubt. He is the first author who has sifted through all the mathematics, history of mathematics, and physics books and collected for us just the material directly related to the Pythagorean theorem."—Robert W. Langer, Professor Emeritus, University of Wisconsin, Eau Claire

Michael C. Fish - Mathematics Teacher

Maor's book is a concise history of the Pythagorean theorem, including the mathematicians, cultures, and people influenced by it. The work is well written and supported by several proofs and exampled from Chinese, Arabic, and European sources the document how these unique cultures came to understand and apply the Pythagorean theorem. [The book] provides thoughtful commentary on the historical connections this fascinating theorem has to many cultures and people.

List of Color Plates     ix
Preface     xi
Prologue: Cambridge, England, 1993     1
Mesopotamia, 1800 BCE     4
Did the Egyptians Know It?     13
Pythagoras     17
Euclid's Elements     32
The Pythagorean Theorem in Art, Poetry, and Prose     45
Archimedes     50
Translators and Commentators, 500-1500 CE     57
Francois Viete Makes History     76
From the Infinite to the Infinitesimal     82
A Remarkable Formula by Euler     94
371 Proofs, and Then Some     98
The Folding Bag     115
Einstein Meets Pythagoras     117
A Most Unusual Proof     119
A Theme and Variations     123
A Pythagorean Curiosity     140
A Case of Overuse     142
Strange Coordinates     145
Notation, Notation, Notation     158
From Flat Space to Curved Spacetime     168
A Case of Misuse     177
Prelude to Relativity     181
From Bern to Berlin, 1905-1915     188
Four Pythagorean Brainteasers     197
But Is It Universal?     201
Afterthoughts     208
Epilogue: Samos, 2005     213
Appendixes
How did the Babylonians Approximate [square root 2?]     219
Pythagorean Triples     221
Sums of Two Squares     223
A Proof that [square root 2] is Irrational     227
Archimedes' Formula for Circumscribing Polygons     229
Proof of some Formulas from Chapter 7     231
Deriving the Equation [Characters not reproducible]     235
Solutions to Brainteasers     237
Chronology     241
Bibliography     247
Illustrations Credits     251
Index     253