Trigonometric Delights

by Eli Maor

Overview

A fun, entertaining exploration of the ideas and people behind the growth of trigonometry

Trigonometry has a reputation as a dry, difficult branch of mathematics, a glorified form of geometry complicated by tedious computation. In Trigonometric Delights, Eli Maor dispels this view. Rejecting the usual descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. From the proto-trigonometry of the Egyptian pyramid builders and the first true trigonometry developed by Greek astronomers, to the epicycles and hypocycles of the toy Spirograph, Maor presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social growth. A tapestry of stories, curiosities, insights, and illustrations, Trigonometric Delights irrevocably changes how we see this essential mathematical discipline.

Product Details

ISBN-13:	9780691202198
Publisher:	Princeton University Press
Publication date:	04/07/2020
Series:	Princeton Science Library , #67
Edition description:	3rd ed.
Pages:	256
Product dimensions:	5.50(w) x 8.50(h) x (d)

About the Author

Eli Maor is a former professor of the history of mathematics at Loyola University Chicago. His books include the internationally acclaimed To Infinity and Beyond, e: The Story of a Number, The Pythagorean Theorem: A 4,000-Year History, and Music by the Numbers (all Princeton).

Table of Contents

Preface
Prologue: Ahmes the Scribe, 1650 B.C.	3
Recreational Mathematics in Ancient Egypt	11
1	Angles	15
2	Chords	20
Plimpton 322: The Earliest Trigonometric Table?	30
3	Six Functions Come of Age	35
Johann Muller alias Regiomonianus	41
4	Trigonometry Becomes Analytic	50
Francois Viete	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
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 Mapmaker's Paradise	165
14	sin x = 2: Imaginary Trigonometry	181
Edmund Landau: The Master Rigorist	192
15	Fourier's Theorem	198
Appendixes	211
1	Let's Revive an Old Idea	213
2	Barrow's Integration of sec [phi]	218
3	Some Trigonometric Gems	220
4	Some Special Values of sin [alpha]	222
Bibliography	225
Credits for Illustrations	229
Index	231

What People are Saying About This

Sean Bradley

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

Nahin

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"

From the Publisher

"If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."—Ian Stewart, New Scientist

"Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."—George H. Swift, American Mathematics Monthly

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover."—Sean Bradley, MAA Online

"This book is full of interesting historical accounts about the development of mathematics."—Richard S. Kitchen, Mathematics Teacher

King

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

Keith Devlin

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"

Kitchen

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

William Durham

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".

Editorial Reviews

"Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."—-George H. Swift, American Mathematics Monthly

From the Publisher

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.

Mathematics Teacher - Richard S. Kitchen

Maor clearly has a great love of trigonometry, formulas and all, and his enthusiasm shines through. . . . If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you.

New Scientist - Ian Stewart

[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition.

MAA Online - Sean Bradley

Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it.

American Mathematics Monthly - George H. Swift

Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it.
— George H. Swift

American Mathematics Monthly