A lively history of the Pythagorean Theorem.
An exploration of one of the most celebrated and well-known theorems in mathematics
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. Although attributed to Pythagoras, the theorem 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 its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
Author(s): Eli Maor
Series: Princeton Science Library; 71
Publisher: Princeton University Press
Year: 2019
Language: English
Pages: 296
Cover
Half title
Imprint
Contents
List of Color Plates
Preface
Prologue: Cambridge, England, 1993
1 Mesopotamia, 1800 bce
Sidebar 1: Did the Egyptians Know It?
2 Pythagoras
3 Euclid’s Elements
Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose
4 Archimedes
5 Translators and Commentators, 500–1500 ce
6 François Viète Makes History
7 From the Infinite to the Infinitesimal
Sidebar 3: A Remarkable Formula by Euler
8 371 Proofs, and Then Some
Sidebar 4: The Folding Bag
Sidebar 5: Einstein Meets Pythagoras
Sidebar 6: A Most Unusual Proof
9 A Theme and Variations
Sidebar 7: A Pythagorean Curiosity
Sidebar 8: A Case of Overuse
10 Strange Coordinates
11 Notation, Notation, Notation
12 From Flat Space to Curved Spacetime
Sidebar 9: A Case of Misuse
13 Prelude to Relativity
14 From Bern to Berlin, 1905–1915
Sidebar 10: Four Pythagorean Brainteasers
15 But Is It Universal?
16 Afterthoughts
Epilogue: Samos, 2005
Appendixes
A. How did the Babylonians Approximate 2 ?
B. Pythagorean Triples
C. Sums of Two Squares
D. A Proof that 2 is Irrational
E. Archimedes’ Formula for Circumscribing Polygons
F. Proof of some Formulas from Chapter 7
G. Deriving the Equation x2/3 + y2/3 = 1
H. Solutions to Brainteasers
I. A Most Unusual Proof
Chronology
Bibliography
Illustrations Credits
Index
