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Trigonometric Delights

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

"If you think trigonometry has no more surprises for you, read Trigonometric Delights. Eli Maor will change your mind. The book presents the subject and its history the way they should be presented--it's a delight to read."--Paul J. Nahin, author of Duelling Idiots and Other Probability Puzzlers

"This book will appeal to a general audience interested in the history of mathematics. I highly recommend [it] to teachers who would like to ground their lessons in the sort of mathematical investigations that were undertaken throughout history."--Richard S. Kitchen, Mathematics Teacher

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, Mathematical Association of America

"Here is trigonometry viewed through the lens of history--a rich, intriguing book that will leave readers shouting for Maor."--William Durham, author of The Mathematical Universe.

"Maor eases the reader from the mathematical puzzles of the Rhind Papyrus all the way to infinite series and the analysis of music produced by vibrating strings. Along the course, he leads a grand tour of the lovely but often neglected area of mathematics called trigonometry."--Jerry P. King, Professor of Mathematics at Lehigh University

"This is a rich and challenging book that will appeal to mathematicians and should help attract a newer generation to the subject. By putting the history back into trigonometry, Maor tells the many stories of trigonometry, and shows that what is often regarded as a collection of dry techniques is really a marvelous testament to thousands of years of human ingenuity and intellectual creativity."--Keith Devlin, author of Mathematics: The Science of Patterns and Goodbye Descartes

Synopsis:

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.

About the Author

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).

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

Product Details

ISBN:
9780691095417
Author:
Maor, Eli
Publisher:
Princeton University Press
Location:
Princeton
Subject:
History
Subject:
Trigonometry
Subject:
History -- Philosophy.
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Mathematics
Subject:
Mathematics-Geometry and Trigonometry
Copyright:
Edition Description:
Trade paper
Publication Date:
February 2002
Binding:
Paperback
Grade Level:
College/higher education:
Language:
English
Illustrations:
101 line drawings 3 halftones
Pages:
256
Dimensions:
9 x 6 in 13 oz

Related Subjects

History and Social Science » Economics » General
History and Social Science » World History » General
Science and Mathematics » Geology » General
Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Trigonometry

Trigonometric Delights
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$ In Stock
Product details 256 pages Princeton University Press - English 9780691095417 Reviews:
"Synopsis" by , "If you think trigonometry has no more surprises for you, read Trigonometric Delights. Eli Maor will change your mind. The book presents the subject and its history the way they should be presented--it's a delight to read."--Paul J. Nahin, author of Duelling Idiots and Other Probability Puzzlers

"This book will appeal to a general audience interested in the history of mathematics. I highly recommend [it] to teachers who would like to ground their lessons in the sort of mathematical investigations that were undertaken throughout history."--Richard S. Kitchen, Mathematics Teacher

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, Mathematical Association of America

"Here is trigonometry viewed through the lens of history--a rich, intriguing book that will leave readers shouting for Maor."--William Durham, author of The Mathematical Universe.

"Maor eases the reader from the mathematical puzzles of the Rhind Papyrus all the way to infinite series and the analysis of music produced by vibrating strings. Along the course, he leads a grand tour of the lovely but often neglected area of mathematics called trigonometry."--Jerry P. King, Professor of Mathematics at Lehigh University

"This is a rich and challenging book that will appeal to mathematicians and should help attract a newer generation to the subject. By putting the history back into trigonometry, Maor tells the many stories of trigonometry, and shows that what is often regarded as a collection of dry techniques is really a marvelous testament to thousands of years of human ingenuity and intellectual creativity."--Keith Devlin, author of Mathematics: The Science of Patterns and Goodbye Descartes

"Synopsis" by , 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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