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# The Pythagorean Theorem

A 4,000-Year History

**Eli Maor **

- Paperback2010Paperback17.9514.95ISBN9780691148236280 pp.6 x 9 1/48 color illus. 141 line illus. 2 tables.Live

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. Maor shows that the theorem, although attributed to Pythagoras, 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 the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

First published in 2007.

*Eli Maor*is the author of

*Venus in Transit*,

*Trigonometric Delights, To Infinity and Beyond*, and

*e: The Story of a Number*(all Princeton). He teaches the history of mathematics at Loyola University in Chicago and at the Graham School of General Education at the University of Chicago.

## More about this book

- Honorable Mention for the 2007 Best Professional/Scholarly Book in Mathematics, Association of American Publishers

## Reviews

**--Ben Longstaff,**

*New Scientist**The Pythagorean Theorem*] is aimed at the reader with an interest in the history of mathematics. It should also appeal to most well-educated people...It is a story based on a theme and guided by a timeline...As a popular account of important ideas and their development, the book should be read by anyone with a good education. It deserves to succeed."

**--Peter M. Neumann,**

*Times Higher Education Supplement**e*, and trigonometry, Maor offers this new work as a comprehensive overview of the Pythagorean Theorem...If one has never read a book by Eli Maor, this book is a great place to start."

**--J. Johnson,**

*Choice***--Amy Shell-Gellasch,**

*MAA Reviews***--Michael C. Fish,**

*Mathematics Teacher***--James J. Tattersull,**

*Mathematical Reviews***--Eric S. Rosenthal,**

*Mathematics Magazine***--Kuldeep,**

*Mathematics and My Diary***--Francis A, Grabowski,**

*European Legacy**The Pythagorean Theorem*is rich in information, careful in its presentation, and at times personal in its approach. . . . The variety of its topics and the engaging way they are presented make

*The Pythagorean Theorem*a pleasure to read."

**--Cecil Rousseau,**

*College Math Journal*## Endorsements

**--Dava Sobel, author of**

*Longitude***--David H. Levy, National Sharing the Sky Foundation**

**--Paul J. Nahin, author of**

*Chases and Escapes*and*Dr. Euler's Fabulous Formula***--Robert W. Langer, Professor Emeritus, University of Wisconsin, Eau Claire**

## Table of Contents

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: François Viète 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

A. How did the Babylonians Approximate? 219

B. Pythagorean Triples 221

C. Sums of Two Squares 223

D. A Proof that is Irrational 227

E. Archimedes' Formula for Circumscribing Polygons 229

F. Proof of some Formulas from Chapter 7 231

G. Deriving the Equation x2/3 ??y2/3 ??1 235

H. Solutions to Brainteasers 237

Chronology 241

Bibliography 247

Illustrations Credits 251

Index 253

## Other Books Written by this Author(s)

- Eli Maor

## Series

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