TABLE OF CONTENTS: Preface xi
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 Müller, alias Regiomontanus 41
4. Trigonometry Becomes Analytic 50
Francois Viète 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 ø 218
3. Some Trigonometric Gems 220
4. Some Special Values of sin α 222
Bibliography 225
Credits for Illustrations 229
Index 231
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