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 42
... fact infinitely many; two 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 ...
... fact, an accuracy equal to that of a modern eight-digit calculator.1 But even more remarkable is the probable purpose of this particular document: by all likelihood, it was intended as an example of how to find the diagonal of any ...
... fact comes to light: this column gives the square of the ratio c/a, that is, the value of csc2 A, where A is the angle opposite side a and csc is the cosecant function studied in trigonometry (fig. 1.4). Let us verify this for line 1 ...
... fact. The pyramids have attracted a cult of worshipers who found in these monuments hidden connections to just about everything in the universe, from the numerical values of π and the Golden Ratio to the alignment of planets and stars ...
... fact that 32 + 42 = 52. But there is no evidence whatsoever to support this hypothesis. It is even less plausible that they used the 3-4-5 rope to construct a right angle, as some authors have stated; it would have been so much easier ...
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 |