Trigonometric Delights

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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.

Author(s): Eli Maor
Publisher: Princeton University Press
Year: 1998

Language: English
Pages: 241

front.pdf......Page 2
preface.pdf......Page 7
prologue.pdf......Page 12
sidebar_a.pdf......Page 20
chapter_1.pdf......Page 24
chapter_2.pdf......Page 29
sidebar_b.pdf......Page 39
chapter_3.pdf......Page 44
sidebar_c.pdf......Page 50
chapter_4.pdf......Page 59
sidebar_d.pdf......Page 65
chapter_5.pdf......Page 72
sidebar_e.pdf......Page 89
chapter_6.pdf......Page 96
chapter_7.pdf......Page 104
sidebar_f.pdf......Page 117
chapter_8.pdf......Page 121
chapter_9.pdf......Page 126
chapter_10.pdf......Page 138
chapter_11.pdf......Page 148
sidebar_g.pdf......Page 154
chapter_12.pdf......Page 159
chapter_13.pdf......Page 174
chapter_14.pdf......Page 190
sidebar_h.pdf......Page 201
chapter_15.pdf......Page 207
appendixes.pdf......Page 220
biblio.pdf......Page 232
credits.pdf......Page 235
index.pdf......Page 236
Preface xi......Page 5