Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. Prologue. Ahmes the Scribe, 1650 B.C. 1
5. Recreational Mathematics in Ancient Egypt 11
6. 1. Angles 15
7. 2. Chords 20
8. Plimpton 322. The Earliest Trigonometric Table? 30
9. 3. Six Functions Come of Age 35
10. Johann Miille, alias Regiomontanus 41
11. 4. Trigonometry Becomes Analytic 50
12. François Vieté 56
13. 5. Measuring Heaven and Earth 63
14. Abraham De Moivre 80
15. 6. Two Theorems from Geometry 87
16. 7. Epicycloids and Hypocycloids 95
17. Maria Agnesi and Her "Witch" 108
18. 8. Variations on a Theme by Gauss 112
19. 9. Had Zeno Only Known This! 117
20. 10. (sin x)/x 129
21. 11. A Remarkable Formula 139
22. Jules Lissajous and His Figures 145
23. 12. tan x 150
24. 13. A Mapmaker's Paradise 165
25. 14. sin x = 2: Imaginary Trigonometry 181
26. Edmund Landau: The Master Rigorist 192
27. 15. Fourier's Theorem 198
28. Appendixes
29. 1. Let's Revive an Old Idea 213
30. 2. Barrow's Integration of sec φ 218
31. 3. Some Trigonometric Gems 220
32. 4. Some Special Values of sin α 222
33. Bibliography 225
34. Credits for Illustrations 229
35. Index 231