The Pythagorean Theorem: A 4,000-Year History (PSL Edition)

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Overview

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.

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Overview

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.

Editorial Reviews

Choice
Based on this recent book, Maor just keeps getting better. Already recognized for his excellent books on infinity, the number 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
MAA Reviews
Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself. . . . Even mathematically savvy readers will gain insights into the inner workings and beauty of mathematics.
— Amy Shell-Gellasch
More Reviews (6) Fewer Reviews
Mathematical Reviews
This book will make for good supplementary reading for high school students, high school teachers, and those with a general interest in mathematics. . . . The author's enthusiasm for his subject is evident throughout the book.
— James J. Tattersull
Mathematics and My Diary
This is an excellent book on the history of the Pythagorean Theorem. . . . This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting. . . . Maor has an exceptional method of writing very technical mathematics in a seamlessly way.
— Kuldeep
Mathematics Magazine
This book goes beyond the theorem and its proofs to set it beautifully in the context of its time and subsequent history.
— Eric S. Rosenthal
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.
— Michael C. Fish
New Scientist
This excellent biography of the theorem is like a history of thought written in lines and circles, moving from ancient clay tablets to Einstein's blackboards. . . . There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction.
— Ben Longstaff
Times Higher Education Supplement
[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

Product Details

  • ISBN-13: 9780691148236
  • Publisher: Princeton University Press
  • Publication date: 7/26/2010
  • Edition description: Reprint
  • Pages: 280
  • Sales rank: 322,232
  • Series: Princeton Science Library Series
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.70 (d)

Meet the Author


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.

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

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

Customer Reviews

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Sort by: Showing all of 2 Customer Reviews

  • Anonymous

    Posted June 17, 2007

    A Book Long Awaited For

    The Pythagorean Theorem is the 'Crown Jewel' of mathematics, and as such, sorely needed a popular exposition. Eli Maor is the first science author in 80 years to step up to this daunting plate! Note: Elisha Loomis wrote his last edition of the Pythagorean Pythagorean Proposition back in the 1920s. Dr. Maor's book is a wealth of information expertly put together in an entertaining and highly readable fashion. As a mathematics teacher for a local community college, I would love to teach a math appreciation course using nothing but Dr. Maor's book since he incorporates so many related ideas and rabbit trails into the major flow of his discourse. Believe me, the Pythagorean Theorem is the underpinning of our modern technical society, forming the basis for everything from cell phones to super-tall skyscrapers to interplanetary probes. In short, we simply can not live our modern technology-filled life without the Pythagorean Theorem. And...any serious student of mathematics needs to understand this via Dr. Maor's book. Go out and purchase, read, and behold!!

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted September 7, 2010

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