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
Results 1-5 of 71
... 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 with the rise of modern algebra, about ...
... length of each leg). But even if we look at the triangle through modern eyes, with one leg placed horizontally and the other vertically (fig. P3), the square on the hypotenuse leaps out of the figure at an odd angle. A beautiful theorem ...
... the Pythagorean theorem: they represent right triangles in which all three sides have integer lengths. So it was only natural that mathematicians tried to go to the next step—find integer solutions of Prologue: Cambridge, England, 1993.
... 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 = a2 + a2 = 2a2)—more ...
... length of the diagonal; or—and this is more plausible—he chose 30 because it is one-half of 60 and therefore lends itself to easy multiplication. In our base-ten system, multiplying a number by 5 can be quickly done by halving 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 |