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Trigonometric Delights, by Eli Maor
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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.
- Sales Rank: #1342116 in Books
- Brand: Brand: Princeton University Press
- Published on: 2002-03-17
- Original language: English
- Number of items: 1
- Dimensions: .62" h x 6.09" w x 9.25" l, .77 pounds
- Binding: Paperback
- 256 pages
- Used Book in Good Condition
Review
"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 Back Cover
"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
About the Author
Eli Maor teaches the history of mathematics at Loyola University in Chicago. He is the author of To Infinity and Beyond, e: The Story of a Number, and June 8, 2004 - Venus in Transit.
Most helpful customer reviews
37 of 40 people found the following review helpful.
generous
By Wyote
This book is really interesting primarily for its information about the history of trigonometry. There's some interesting stuff about the ancient Egyptians, Babylonians and Greeks; and a lot of great stuff about early European mathematics; stopping around Euler's time.
I hadn't studied trig in about 8 years, and I thought this would be a good review. Boy, was I wrong! I needed to do the review and then study this book!
Anyway, if you're a fairly gifted high school trig student, this book will certainly liven up the subject for you. If you're a college math major, it will be easy reading, and certainly interesting. If you're a teacher, you might find something interesting to entertain your students. Otherwise, unless you really like math or are really good at it, this book will probably be really difficult for you.
When I was feeling lazy I kind of breezed through the dense equations and looked for the conclusions, but when I was diligent I could usually make sense of them. You can do as I did and you won't miss much. Really, the highlights of the book are the historical information, not the equations. But if you can appreciate the equations as well, then you'll probably really enjoy the book.
Of course this isn't a life-changing or eye-opening book, but I gave it 5 stars just so no one thinks there's anything wrong with it.
0 of 0 people found the following review helpful.
Five Stars
By Sam Tobin
I love it.
17 of 17 people found the following review helpful.
Off On A Good Tangent
By Michael LaDeau
The latest of a series by Eli Maor, this one is my favorite.
For those who need more warming up to the mathematics, I would recommend reading Maor's earlier books first. Infinity and Beyond, The Story of a Number (e), and Trigonometric Delights have some overlapping subject matter. And, the author develops them in later books with new concepts. Although there is some content overlap (perhaps five percent), there is plenty original content in each book.
The main reason this book is a favorite of mine is due to the subject, trigonometry is not covered so well by others. Also, this book has a more refined format than his earlier books. High school trigonometry, rarely taught in depth today, is good enough to make this an easy read. For young adults who have suffered the modern brush over, this book is priceless. For all readers, this book offers a fresh perspective. You will see the practical applications; and you will truly learn the purpose of a trigonometric function. If you appreciate graphical representations, you will appreciate this author's approach..
As in his earlier work's subject matter, Maor gives a good history of this subject matter. But, geometric solutions to problems are the gems of this book. Regiomontaus's maximum problem, a geometric solution to Zeno's paradox, and a geometric construction of an infinite product are developed. Also described is the contribution of trigonometry to the infinite series and De Moivre's theorem. If you ever owned a Spirograph, you will have wished a copy of this book to truly visualize what those circles and gears were truly doing and to learn to predict results through math.
Any book by Eli Maor would not be complete without concepts of conformal mapping as applied to mapmaking. In this book, he cleverly shows in detail the conversion of a spherical map to a flat one while explaining the virtues of conformal mapping. In the penultimate chapter Sinx = 2, Imaginary Trigonometry, Maor illustrates the link between trigonometry, imaginary numbers, and the complex plane. Nowhere else have I seen a better description of conformal mapping of a complex valued function. The book's final chapter is a clear and interesting illustration of Fourier's theorem. These last two chapters contain the most challenging concepts; but they are clearly explained.
I hope for another book by this author to be published soon.
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