The Pythagorean Theorem: A 4,000-Year HistoryAn exploration of one of the most celebrated and well-known theorems in mathematics |
From inside the book
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... example, the three altitudes of a triangle: they always meet at one point (as do the medians and the angle bisectors). This statement has a certain elegance to it, with its sweeping symmetry: no side or vertex takes precedence over any ...
... example, trigonometry, a subject notorious for its seemingly endless supply of formulas. Whether it is sin2 x + cos2 x = 1, or 1 + tan2 x = sec2 x, or 1 + cot2 x = csc2 x, these identities are the ghosts of the Pythagorean theorem ...
... examples are (3, 4, 5) and (5, 12, 13). Such triples, of course, immediately remind us of the Pythagorean theorem: they represent right triangles in which all three sides have integer lengths. So it was only natural that mathematicians ...
... were marked with similar notches written horizontally. Let us denote these symbols by | and —, respectively. The number 23, for example, would be written as — — |||. When a number exceeded 59, Figure 1.1. YBC 7289 1 Mesopotamia, 1800 BCE.
... example just given, the numerals — — — — — could also stand for 40 × 602 + 13 × 60 = 144,780; or they could mean 40/60 + 13 = 13.666, or any other combination of powers of 60 with the coefficients 40 and 13. Moreover, had the ...
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 |