The Pythagorean Theorem: A 4,000-Year History

The Pythagorean Theorem: A 4,000-Year History

by Eli Maor


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An exploration of one of the most celebrated and well-known theorems in mathematics

By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof—if indeed he had one—is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

Product Details

ISBN-13: 9780691196886
Publisher: Princeton University Press
Publication date: 11/19/2019
Series: Princeton Science Library , #65
Edition description: Reprint
Pages: 296
Sales rank: 1,150,468
Product dimensions: 5.50(w) x 8.40(h) x 0.90(d)
Age Range: 14 - 17 Years

About the Author

Eli Maor is the author of seven books, including Music by the Numbers, Trigonometric Delights, To Infinity and Beyond, and e: The Story of a Number (all Princeton). He is a former professor of the history of mathematics at Loyola University Chicago.

Table of Contents

List of Color Plates ix
Preface xi
Prologue: Cambridge, England, 1993 1
Chapter 1: Mesopotamia, 1800 bce 4
Sidebar 1: Did the Egyptians Know It? 13
Chapter 2: Pythagoras 17
Chapter 3: Euclid's Elements 32
Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose 45
Chapter 4: Archimedes 50
Chapter 5: Translators and Commentators, 500-1500 ce 57
Chapter 6: Fran ois Vi te Makes History 76
Chapter 7: From the Infinite to the Infinitesimal 82
Sidebar 3: A Remarkable Formula by Euler 94
Chapter 8: 371 Proofs, and Then Some 98
Sidebar 4: The Folding Bag 115
Sidebar 5: Einstein Meets Pythagoras 117
Sidebar 6: A Most Unusual Proof 119
Chapter 9: A Theme and Variations 123
Sidebar 7: A Pythagorean Curiosity 140
Sidebar 8: A Case of Overuse 142
Chapter 10: Strange Coordinates 145
Chapter 11: Notation, Notation, Notation 158
Chapter 12: From Flat Space to Curved Spacetime 168
Sidebar 9: A Case of Misuse 177
Chapter 13: Prelude to Relativity 181
Chapter 14: From Bern to Berlin, 1905-1915 188
Sidebar 10: Four Pythagorean Brainteasers 197
Chapter 15: But Is It Universal? 201
Chapter 16: Afterthoughts 208
Epilogue: Samos, 2005 213
Appendixes 219-237
Chronology 241
Bibliography 247
Illustrations Credits 251
Index 253

What People are Saying About This


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


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

Dava Sobel

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"


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"

From the Publisher

"If one has never read a book by Eli Maor, this book is a great place to start."—J. Johnson, Choice

"Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself."—Amy Shell-Gellasch, MAA Reviews

"A popular account of important ideas and their development."—Peter M. Neumann, Times Higher Education Supplement

"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

"There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."—Ben Longstaff, New Scientist

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