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.

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.


Off On A Good Tangent   May 27, 2006
Michael LaDeau (Texas)
8 out of 8 found this review helpful

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.


Simply Delightful   January 24, 2003
H. Ting (College Park, Maryland)
14 out of 16 found this review helpful

What do sines, pyramids, music, and Fourier series all have in common? Eli Maor did an excellent job in explaining these dry and seemingly irrelevant terminologies to his readers. From Ahmes the Scribe to Fourier, Maor traced the development of trigonometry by juxtaposing different trig concepts with people and anecdotes. An inspiratoinal book.


Wish They Had 10 Star Ratings!   January 11, 2007
Scott Lewis (Memphis, TN)
4 out of 4 found this review helpful

I accidentally stumbled upon this book when looking up "hypocycloids." This book literally blew me away! How many books do you know of that addresses De'Moivre's Theorem....and shows you how to use it? And, this little book also gives you the history of the concepts.

This book starts out taking you on a trip thru Ancient Egypt and trigonometry's roots. It dissects a pyramid, mathematically. Cool. It then explores all facets of trigonometry from a fun point of view.

You can't help but love this book. I can hardly put it down. So, if you ever want to know "why" you are doing anything trigonometrically, then this book is for you. Total amateur or PhD level person will love this little book!


Inspirational!   July 21, 2000
Helmer Aslaksen (Singapore)
11 out of 19 found this review helpful

If you think that trigonometry is boring and trivial, then read this book! He shows how central trig has been to many fields of math and science. A truly inspirational book!