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The Pythagorean Theorem : A 4,000-Year History - Eli Maor

The Pythagorean Theorem

A 4,000-Year History

By: Eli Maor

Paperback Published: 15th August 2010
ISBN: 9780691148236
Number Of Pages: 280
For Ages: 14 - 17 years old

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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.

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 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, MAA Reviews "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 "All in all, this affordable book, as with Maor's previous titles, is rollicking good fun and highly recommended to anyone with even the slightest interest in the history of mathematics."--Francis A, Grabowski, European Legacy "The Pythagorean Theorem is rich in information, careful in its presentation, and at times personal in its approach... The variety of its topics and the engaging way they are presented make The Pythagorean Theorem a pleasure to read."--Cecil Rousseau, College Math Journal

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: Francois Viete 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

ISBN: 9780691148236
ISBN-10: 0691148236
Series: Princeton Science Library
Audience: Professional
For Ages: 14 - 17 years old
For Grades: 9 - 12
Format: Paperback
Language: English
Number Of Pages: 280
Published: 15th August 2010
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.45
Edition Type: Revised

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