Trigonometric Delights / Edition 1

Trigonometric Delights / Edition 1

5.0 1
by Eli Maor
     
 

ISBN-10: 0691095418

ISBN-13: 9780691095417

Pub. Date: 02/25/2002

Publisher: Princeton University Press

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…  See more details below

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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Product Details

ISBN-13:
9780691095417
Publisher:
Princeton University Press
Publication date:
02/25/2002
Edition description:
REPRINT
Pages:
256
Product dimensions:
5.99(w) x 8.95(h) x (d)

Table of Contents

Preface
Prologue: Ahmes the Scribe, 1650 B.C.3
Recreational Mathematics in Ancient Egypt11
1Angles15
2Chords20
Plimpton 322: The Earliest Trigonometric Table?30
3Six Functions Come of Age35
Johann Muller alias Regiomonianus41
4Trigonometry Becomes Analytic50
Francois Viete56
5Measuring Heaven and Earth63
Abraham De Moivre80
6Two Theorems from Geometry87
7Epicycloids and Hypocycloids95
Maria Agnesi and Her "Witch"108
8Variations on a Theme by Gauss112
9Had Zeno Only Known This!117
10(sin x) / x129
11A Remarkable Formula139
Jules Lissajous and His Figures145
12tan x150
13A Mapmaker's Paradise165
14sin x = 2: Imaginary Trigonometry181
Edmund Landau: The Master Rigorist192
15Fourier's Theorem198
Appendixes211
1Let's Revive an Old Idea213
2Barrow's Integration of sec [phi]218
3Some Trigonometric Gems220
4Some Special Values of sin [alpha]222
Bibliography225
Credits for Illustrations229
Index231

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