Enhanced descriptions from Syndetics:

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.

Table of contents provided by Syndetics

• Preface
• Prologue: Ahmes the Scribe, 1650 B.C. (p. 3)
• Recreational Mathematics in Ancient Egypt (p. 11)
• 1 Angles (p. 15)
• 2 Chords (p. 20)
• Plimpton 322: The Earliest Trigonometric Table? (p. 30)
• 3 Six Functions Come of Age (p. 35)
• Johann Muller alias Regiomonianus (p. 41)
• 4 Trigonometry Becomes Analytic (p. 50)
• Francois Viete (p. 56)
• 5 Measuring Heaven and Earth (p. 63)
• Abraham De Moivre (p. 80)
• 6 Two Theorems from Geometry (p. 87)
• 7 Epicycloids and Hypocycloids (p. 95)
• Maria Agnesi and Her "Witch" (p. 108)
• 8 Variations on a Theme by Gauss (p. 112)
• 9 Had Zeno Only Known This! (p. 117)
• 10 (sin x) / x (p. 129)
• 11 A Remarkable Formula (p. 139)
• Jules Lissajous and His Figures (p. 145)
• 12 tan x (p. 150)
• 13 A Mapmaker's Paradise (p. 165)
• 14 sin x = 2: Imaginary Trigonometry (p. 181)
• Edmund Landau: The Master Rigorist (p. 192)
• 15 Fourier's Theorem (p. 198)
• Appendixes (p. 211)
• 1 Let's Revive an Old Idea (p. 213)
• 2 Barrow's Integration of sec [phi] (p. 218)
• 3 Some Trigonometric Gems (p. 220)
• 4 Some Special Values of sin [alpha] (p. 222)
• Bibliography (p. 225)
• Credits for Illustrations (p. 229)
• Index (p. 231)

Reviews provided by Syndetics

CHOICE Review

Maor (history of mathematics, Loyola Univ.) writes to dispel the view that trigonometry is merely "glorified geometry with superimposed computational torture." Trigonometric Delights is just that: a series of short, largely independent, well-written riffs on trigonometric themes. In particular, there is much historical material, ranging from the Egyptian and Babylonian period to the early 19th century. Maor tells the reader about the "proto-trigonometry" of pyramid-building Egyptians, Greek astronomers working on true trigonometry, and Renaissance European analytical trigonometry and its influence on the development of accurate artillery, precise clocks, and more pleasing musical instruments. Maor describes the work of mapmaker Gerardus Mercator, M.C. Escher's fanciful artwork, the Renaissance scholar Regiomontanus, and mathematician Maria Agnesi and her famous curve, the "Witch of Agnesi." While it is not clear that anyone can really make trigonometry appetizing, Maor has assembled some lovely material that will be accessible to anyone who has had a course in trigonometry. General readers. M. Henle; Oberlin College

Author notes provided by Syndetics

Eli Maor is a teacher of the history of mathematics who has successfully popularized his subject with the general public through a series of informative and entertaining books.

In "E: The Story of a Number," Maor uses anecdotes, excursions and essays to illustrate that number's importance to mathematics. "Trigonometric Delights" brings trigonometry to life by blending history, biography, scientific curiosities and mathematics to achieve the goal of showing how trigonometry has contributed to both science and social development. "To Infinity and Beyond: A Cultural History of the Infinite" explores the idea of infinity in mathematics and art through the use of the illustrations of the Dutch artist M.C. Escher.

Eli Maor's readable books have made the world of numbers accessible even to those with little or no background in mathematics.

(Bowker Author Biography)