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Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the ...
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.
Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles.
Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.
"[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
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
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
Credits for Illustrations 229
Posted October 5, 2013
Posted March 26, 2013
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