Trigonometric Delights

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Princeton University Press, 2002 - 236 pàgines
1 Ressenya

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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Revisió d'Usuari  - jefware - LibraryThing

Maor is always good for a few back stories and elegant alternative proofs. Really best experiences during or right after a class in trigonometry, He makes the characters from the history of trigonomrtry come alive in a nerdy sort of way. Llegeix la ressenya completa

Continguts

Ahmes the Scribe 1650 BC
3
Recreational Mathematics in Ancient Egypt
11
1 Angles
15
2 Chords
20
The Earliest Trigonometric Table?
30
3 Six Functions Come of Age
35
Johann Müller alias Regiomontanus
41
4 Trigonometry Becomes Analytic
50
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 Mapmakers Paradise
165
Imaginary Trigonometry
181
The Master Rigorist
192

François Viète
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
15 Fouriers Theorem
198
Appendixes
211
Bibliography
225
Credits for Illustrations
229
Index
231
Copyright

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Quant a l’autor (2002)

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).

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