The Pythagorean Theorem: A 4,000-Year History (Princeton Science Library)

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. The Pythagorean Theorem......Page 2 Copyright......Page 5 Contents......Page 8 List ol Color Plates......Page 10 Preface......Page 12 Prologue: Cambridge, England, 1993......Page 20 1 Mesopotamia, 1800 BCE......Page 23 Sidebar 1: Did the Egyptians Know It?......Page 32 2 Pythagoras......Page 36 3 Euclid's Elements......Page 51 Sidebar 2: The Pythagorean Theorem in Art, Poetry,and Prose......Page 64 4 Archimedes......Page 69 5 Translators and Commentators, 500-1500 CE......Page 76 6 François Viète Makes History......Page 95 7 From the Infinite to the Infinitesimal......Page 101 Sidebar 3: A Remarkable Formula by Euler......Page 113 8 371 Proofs, and Then Some......Page 117 Sidebar 4: The Folding Bag......Page 134 Sidebar 5: Einstein Meets Pythagoras......Page 136 Sidebar 6: A Most Unusual Proof......Page 138 9 A Theme and Variations......Page 142 Sidebar 7: A Pythagorean Curiosity......Page 167 Sidebar 8: A Case of Overuse......Page 169 10 Strange Coordinates......Page 172 11 Notation, Notation, Notation......Page 185 12 From Flat Space to Curved Spacetime......Page 195 Sidebar 9: A Case of Misuse......Page 204 13 Prelude to Relativity......Page 208 14 From Bern to Berlin, 1905-1915......Page 215 Sidebar 10: Four Pythagorean Brainteasers......Page 224 15 But Is It Universal?......Page 228 16 Afterthoughts......Page 235 Epilogue: Samos, 2005......Page 240 A. How did the Babylonians Approximate ✓2?......Page 246 B. Pythagorean Triples......Page 248 C. Sums of Two Squares......Page 250 D. A Proof That ✓2 Is Irrational......Page 254 E. Archimedes' Formula for Circumscribing Polygons......Page 256 F. Proofs of Some Formulas from Chapter 7......Page 258 G. Deriving the Equation x2/3 + y2/3 = 1......Page 262 Chronology......Page 268 Bibliography......Page 274 Illustrations Credits......Page 278 Index......Page 280 About the Type......Page 288 The Pythagorean Theorem 2 Copyright 5 Contents 8 List ol Color Plates 10 Preface 12 Prologue: Cambridge, England, 1993 20 1 Mesopotamia, 1800 BCE 23 Sidebar 1: Did the Egyptians Know It? 32 2 Pythagoras 36 3 Euclid's Elements 51 Sidebar 2: The Pythagorean Theorem in Art, Poetry,and Prose 64 4 Archimedes 69 5 Translators and Commentators, 500-1500 CE 76 6 François Viète Makes History 95 7 From the Infinite to the Infinitesimal 101 Sidebar 3: A Remarkable Formula by Euler 113 8 371 Proofs, and Then Some 117 Sidebar 4: The Folding Bag 134 Sidebar 5: Einstein Meets Pythagoras 136 Sidebar 6: A Most Unusual Proof 138 9 A Theme and Variations 142 Sidebar 7: A Pythagorean Curiosity 167 Sidebar 8: A Case of Overuse 169 10 Strange Coordinates 172 11 Notation, Notation, Notation 185 12 From Flat Space to Curved Spacetime 195 Sidebar 9: A Case of Misuse 204 13 Prelude to Relativity 208 14 From Bern to Berlin, 1905-1915 215 Sidebar 10: Four Pythagorean Brainteasers 224 15 But Is It Universal? 228 16 Afterthoughts 235 Epilogue: Samos, 2005 240 Appendix 246 A. How did the Babylonians Approximate ✓2? 246 B. Pythagorean Triples 248 C. Sums of Two Squares 250 D. A Proof That ✓2 Is Irrational 254 E. Archimedes' Formula for Circumscribing Polygons 256 F. Proofs of Some Formulas from Chapter 7 258 G. Deriving the Equation x2/3 + y2/3 = 1 262 Chronology 268 Bibliography 274 Illustrations Credits 278 Index 280 About the Type 288 ISBN:,978-0-691-12526-8 ISBN: 978-0-691-12526-8 By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here - perhaps for the first time in English - is the full story of this famous theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof - if indeed he had one - is lost to us. Euclid immortalized it as Proposition 47 in his Elements, and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity. In this book, Eli 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 Prologue: Cambridge, England, 1993 -- Mesopotamia, 1800 Bce -- Sidebar 1: Did The Egyptians Know It? -- Pythagoras -- Euclid's Elements -- Sidebar 2: The Pythagorean Theorem In Art, Poetry, And Prose -- Archimedes -- Translators And Commentators, 500-1500 Ce -- François Viète Makes History -- From The Infinite To The Infinitesimal -- Sidebar 3: A Remarkable Formula By Euler -- 371 Proofs, And Then Some -- Sidebar 4: The Folding Bag -- Sidebar 5: Einstein Meets Pythagoras -- Sidebar 6: A Most Unusual Proof -- A Theme And Variations -- Sidebar 7: A Pythagorean Curiosity -- Sidebar 8: A Case Of Overuse -- Strange Coordinates -- Notation, Notation, Notation -- From Flat Space To Curved Spacetime -- Sidebar 9: A Case Of Misuse -- Prelude To Relativity -- From Bern To Berlin, 1905-1915 -- Sidebar 10: Four Pythagorean Brainteasers -- But Is It Universal? -- Afterthoughts -- Epilogue: Samos, 2005. Eli Maor. Includes Bibliographical References (p. [247]-250) And Index. By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, the author reveals the full story of this ubiquitous geometric theorem. It shows that the theorem, although attributed to Pythagoras, was known to the Babylonians more than a thousand years earlier. The author presents a complex history of the Pythagorean Theorem, examining the earliest evidence of knowledge of the theorem to Einstein's theory of relativity