Trigonometric Delights (ebook)

Argumento de Trigonometric Delights (ebook)

"If you think trigonometry has no more surprises for you, read Trigonometric Delights. Eli Maor will change your mind. The book presents the subject and its history the way they should be presented--it's a delight to read."--Paul J. Nahin, author of Duelling Idiots and Other Probability Puzzlers

"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

"Here is trigonometry viewed through the lens of history--a rich, intriguing book that will leave readers shouting for Maor."--William Durham, author of The Mathematical Universe.

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, Mathematical Association of America

"Maor eases the reader from the mathematical puzzles of the Rhind Papyrus all the way to infinite series and the analysis of music produced by vibrating strings. Along the course, he leads a grand tour of the lovely but often neglected area of mathematics called trigonometry."--Jerry P. King, Professor of Mathematics at Lehigh University

"This is a rich and challenging book that will appeal to mathematicians and should help attract a newer generation to the subject. By putting the history back into trigonometry, Maor tells the many stories of trigonometry, and shows that what is often regarded as a collection of dry techniques is really a marvelous testament to thousands of years of human ingenuity and intellectual creativity."--Keith Devlin, author of Mathematics: The Science of Patterns and Goodbye Descartes

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, MAA Online

"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 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 Teacher0Preface 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 ? 222
Bibliography 225
Credits for Illustrations 229
Index 231