Buch, Englisch, 280 Seiten, Format (B × H): 155 mm x 232 mm, Gewicht: 481 g
Reihe: Princeton Science Library
A 4,000-Year History
Buch, Englisch, 280 Seiten, Format (B × H): 155 mm x 232 mm, Gewicht: 481 g
Reihe: Princeton Science Library
ISBN: 978-0-691-14823-6
Verlag: Princeton University Press
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.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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: Fran?ois Vi?te 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
