The Pythagorean Theorem: A 4,000-year History

The Pythagorean Theorem: A 4,000-year History

Hardback

By (author) Eli Maor

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  • Publisher: Princeton University Press
  • Format: Hardback | 288 pages
  • Dimensions: 158mm x 236mm x 28mm | 522g
  • Publication date: 1 June 2007
  • Publication City/Country: New Jersey
  • ISBN 10: 0691125260
  • ISBN 13: 9780691125268
  • Illustrations note: 8 color plates. 141 line illus. 2 tables.
  • Sales rank: 384,524

Product description

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.

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Author information

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).

Review quote

Honorable Mention for the 2007 Best Professional/Scholarly Book in Mathematics, Association of American Publishers "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, 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 "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, Choice "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, Mathematics Teacher "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, Mathematical Reviews "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 Magazine "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 and My Diary

Flap copy

"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 a + b = c, 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

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: Franois Vite 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