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 Muller, alias Regiomontanus 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 o 218 3.Some Trigonometric Gems 220 4.Some Special Values of sin alpha 222 Bibliography 225 Credits for Illustrations 229 Index 231

About the Author

Eli Maor teaches the history of mathematics at Loyola University in Chicago. He is the author of "To Infinity and Beyond", "e: The Story of a Number", "Venus in Transit", and "The Pythagorean Theorem: A 4,000-Year History".

Reviews

"Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."--George H. Swift, American Mathematics Monthly "[Maor] writes enthusiastically and engagingly... Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, MAA Online "Maor clearly has a great love of trigonometry, formulas and all, and his enthusiasm shines through... If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."--Ian Stewart, New Scientist "This book will appeal to a general audience interested in the history of mathematics. I highly recommend [it] to teachers who would like to ground their lessons in the sort of mathematical investigations that were undertaken throughout history."--Richard S. Kitchen, Mathematics Teacher