Trigonometric Delights

Eli Maor

250 pages, parution le 06/12/2002

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Résumé

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.

Contents

Angles
Chords
Six Functions Come of Age
Trigonometry Becomes Analytic
Measuring Heaven and Earth
Two Theorems from Geometry
Epicycloids and Hypocycloids
Variations on a Theme by Gauss
Had Zeno Only Known This!
(sin x) / x
A Remarkable Formula
tan x
A Mapmaker's Paradise
sin x = 2: Imaginary Trigonometry
Fourier's Theorem

Appendixes
Let's Revive an Old Idea
Barrow's Integration of sec [phi]
Some Trigonometric Gems
Some Special Values of sin [alpha]

L'avis du libraire Eyrolles

La trigonométrie a la réputation d'une matière austère. Cet ouvrage nous la fait découvrir sous un jour différent. On l'apprécie au travers de ses applications les plus étonnantes : art, musique, architecture...

L'auteur - Eli Maor

Eli Maor teaches the history of mathematics at Loyola University in Chicago. He has published extensively in journals of mathematics and mathematics education and is the author of To Infinity and Beyond , e: The Story of a Number, and June 8, 2004--Venus in Transit (all Princeton).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Eli Maor
Parution	06/12/2002
Nb. de pages	250
Format	15,5 x 23,5
Couverture	Broché
Poids	366g
Intérieur	Noir et Blanc
EAN13	9780691095417
ISBN13	978-0-691-09541-7