The Pythagorean Theorem: A 4,000-Year HistoryAn exploration of one of the most celebrated and well-known theorems in mathematics |
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... relation, a2 + b2 = c2, from which the length of one side of a right triangle can be found, given the lengths of the other two sides. But that is not how Pythagoras viewed it; to him it was a geometric statement about areas. It was only ...
... is drawn, the product PA × PB is constant—it has the same value for all chords through P (fig. P2). Again we have perfect democracy: every chord has the same status in relation to P as any other. C A D B P Figure P2. PA × PB xii Preface ❖
... relation between the length of the diagonal of a square and its side, d = a 2 . But this in turn means that they were familiar with the Pythagorean theorem—or at the very least, with its special case for the diagonal of a square (d2 ...
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Contents
1 | |
4 | |
2 Pythagoras | 17 |
3 Euclids Elements | 32 |
4 Archimedes | 50 |
5 Translators and Commentators 5001500 CE | 57 |
6 François Viète Makes History | 76 |
7 From the Infinite to the Infinitesimal | 82 |
12 From Flat Space to Curved Spacetime | 168 |
13 Prelude to Relativity | 181 |
14 From Bern to Berlin 19051915 | 188 |
15 But Is It Universal? | 201 |
16 Afterthoughts | 208 |
Samos 2005 | 213 |
Appendixes | 219 |
Chronology | 245 |
8 371 Proofs and Then Some | 98 |
9 A Theme and Variations | 123 |
10 Strange Coordinates | 145 |
11 Notation Notation Notation | 158 |
Bibliography | 251 |
Illustrations Credits | 255 |
Index | 257 |