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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.
|Publisher:||Princeton University Press|
|Product dimensions:||6.30(w) x 9.30(h) x 1.10(d)|
|Age Range:||14 - 17 Years|
About the Author
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).
Table of Contents
List of Color Plates ix
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
Illustrations Credits 251
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
At last, a popular book that isn't afraid to print a mathematical formula in all its symbolic glory! Thanks to Eli Maor for provingin his delightful, playful waythe 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"