The Pythagorean Theorem: A 4,000-Year History
296
The Pythagorean Theorem: A 4,000-Year History
296Paperback(Reprint)
-
PICK UP IN STORECheck Availability at Nearby Stores
Available within 2 business hours
Related collections and offers
Overview
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.
Product Details
| ISBN-13: | 9780691196886 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 11/19/2019 |
| Series: | Princeton Science Library , #65 |
| Edition description: | Reprint |
| Pages: | 296 |
| Sales rank: | 485,628 |
| Product dimensions: | 5.50(w) x 8.40(h) x 0.90(d) |
| Age Range: | 14 - 17 Years |
About the Author
Table of Contents
List of Color Plates ix
Preface xi
Prologue: Cambridge, England, 1993 1
Mesopotamia, 1800 BCE 4
Did the Egyptians Know It? 13
Pythagoras 17
Euclid's Elements 32
The Pythagorean Theorem in Art, Poetry, and Prose 45
Archimedes 50
Translators and Commentators, 500-1500 CE 57
Francois Viete Makes History 76
From the Infinite to the Infinitesimal 82
A Remarkable Formula by Euler 94
371 Proofs, and Then Some 98
The Folding Bag 115
Einstein Meets Pythagoras 117
A Most Unusual Proof 119
A Theme and Variations 123
A Pythagorean Curiosity 140
A Case of Overuse 142
Strange Coordinates 145
Notation, Notation, Notation 158
From Flat Space to Curved Spacetime 168
A Case of Misuse 177
Prelude to Relativity 181
From Bern to Berlin, 1905-1915 188
Four Pythagorean Brainteasers 197
But Is It Universal? 201
Afterthoughts 208
Epilogue: Samos, 2005 213
Appendixes
How did the Babylonians Approximate [square root 2?] 219
Pythagorean Triples 221
Sums of Two Squares 223
A Proof that [square root 2] is Irrational 227
Archimedes' Formula for Circumscribing Polygons 229
Proof of some Formulas from Chapter 7 231
Deriving the Equation [Characters not reproducible] 235
Solutions to Brainteasers 237
Chronology 241
Bibliography 247
Illustrations Credits 251
Index 253
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 proving—in his delightful, playful way—the 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"
"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 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"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