The Pythagorean theorem - a 4,000-year history.

288 Pages·2010·29.401 MB·English

by  Maor, Eli

The Pythagorean Theorem
A
C B
The simplest known proof of the Pythagorean theorem
(see p. 115)
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Copyright © 2007 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
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All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Maor, Eli.
The Pythagorean theorem : a 4,000-year history / Eli Maor.
p. cm.
Includes bibliographical references and index.
ISB3N: 9-78I-0 -691-12526-8 (acid-free paper)
ISB0N: 0--6I91 -12526-0 (acid-free paper)
I. Pythagorean theorem-History. I. Title.
QA460.P8M36 2007
516.22--dc22 2006050969
British Library Cataloging-in-Publication Data is available
This book has been composed in Times
Printed on acid-free paper.
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Contents
List of Color Plates
IX
Preface
XI
Prologue: Cambridge, England, 1993
I
I
Mesopotamia, 1800
BCE
4
Sidebar 1:
13
Did the Egyptians Know It?
2
Pythagoras
17
3
Euclid's Elements
32
Sidebar 2:
The Pythagorean Theorem in Art, Poetry,
45
and Prose
4
Archimedes
50
5
Translators and Commentators, 500-1500
CE
57
6
Fran�ois Viete Makes History
76
7
From the Infinite to the Infinitesimal
82
Sidebar 3:
94
A Remarkable Formula by Euler
8
371 Proofs, and Then Some
98
Sidebar 4:
115
The Folding Bag
Sidebar 5:
117
Einstein Meets Pythagoras
Sidebar 6:
119
A Most Unusual Proof
9
A Theme and Variations
123
Sidebar 7:
140
A Pythagorean Curiosity
Sidebar 8:
142
A Case of Overuse
Strange Coordinates
IO
145
II
Notation, Notation, Notation
158
...
....
•
Contents
Vlll
From Flat Space to Curved Spacetime
12 168
Sidebar 9: A Case of Misuse
177
Prelude to Relativity
13 181
From Bern to Berlin, 1905-1915
14 188
Sidebar 10: Four Pythagorean Brainteasers
197
But Is It Universal?
15 201
Afterthoughts
16 208
213
Epilogue: Samos, 2005
Appendixes
✓2
A. How did the Babylonians Approximate ?
219
Pythagorean Triples
B. 221
Sums of Two Squares
C. 223
✓2
A Proof that is Irrational
D. 227
E. Archimedes' Formula for Circumscribing Polygons
229
F. Proof of some Formulas from Chapter
7 231
Deriving the Equation 213 + 213 = I
G. 235
x y
Solutions to Brainteasers
H. 237
241
Chronology
247
Bibliography
251
Illustrations Credits
253
Index
List ol Color Plates
Color illustrations follow page 134.
Plate 1.
Postal stamps honoring Pythagoras and
his contemporaries (Robin J. Wilson).
Plate 2.
The Pythagorean theorem in an Arab text (Mankiewicz)
Plate 3.
"The Cloud Gate" at the Millennium Park, Chicago
Plate 4.
Aristarhos of Samas Airport
Plate 5.
Pythagorio, Samas: the harbor
Plate 6.
Pythagorio: Gymnasia Pythagoreio
Plate 7.
Pythagorio: Pythagora Street
Plate 8.
Pythagorio: statue of Pythagoras
Plate 9.
Karlovasi, Samas: statue of Aristarchus
Note: all photographs are courtesy of the author, except where noted.