Trigonometric Delights / Edition 1

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Overview

Trigonometry has always been the black sheep 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.

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Editorial Reviews

American Mathematics Monthly
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'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 - George H. Swift
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.
MAA Online - Sean Bradley
[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition.
New Scientist - Ian Stewart
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.
Mathematics Teacher - Richard S. Kitchen
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.
From the Publisher

"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

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Product Details

  • ISBN-13: 9780691095417
  • Publisher: Princeton University Press
  • Publication date: 2/25/2002
  • Edition description: REPRINT
  • Edition number: 1
  • Pages: 256

Meet 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".
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Table of Contents

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
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