| Preface | |
| Prologue: Ahmes the Scribe, 1650 B.C. | 3 |
| Recreational Mathematics in Ancient Egypt | 11 |
| 1 | Angles | 15 |
| 2 | Chords | 20 |
| Plimpton 322: The Earliest Trigonometric Table? | 30 |
| 3 | Six Functions Come of Age | 35 |
| Johann Muller alias Regiomonianus | 41 |
| 4 | Trigonometry Becomes Analytic | 50 |
| Francois Viete | 56 |
| 5 | Measuring Heaven and Earth | 63 |
| Abraham De Moivre | 80 |
| 6 | Two Theorems from Geometry | 87 |
| 7 | Epicycloids and Hypocycloids | 95 |
| Maria Agnesi and Her "Witch" | 108 |
| 8 | Variations on a Theme by Gauss | 112 |
| 9 | Had Zeno Only Known This! | 117 |
| 10 | (sin x) / x | 129 |
| 11 | A Remarkable Formula | 139 |
| Jules Lissajous and His Figures | 145 |
| 12 | tan x | 150 |
| 13 | A Mapmaker's Paradise | 165 |
| 14 | sin x = 2: Imaginary Trigonometry | 181 |
| Edmund Landau: The Master Rigorist | 192 |
| 15 | Fourier's Theorem | 198 |
| Appendixes | 211 |
| 1 | Let's Revive an Old Idea | 213 |
| 2 | Barrow's Integration of sec [phi] | 218 |
| 3 | Some Trigonometric Gems | 220 |
| 4 | Some Special Values of sin [alpha] | 222 |
| Bibliography | 225 |
| Credits for Illustrations | 229 |
| Index | 231 |
