Customer Reviews

Trigonometric Delights

5 star:		(9)
4 star:		(2)
3 star:		(0)
2 star:		(1)
1 star:		(1)

 

 

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.

On the whole, this was a pleasant read. I'll try to give a sense of where the highlights are and aren't, since the book could have used some more rigorous editing to make it more uniformly good.

The bits on the early history of trigonometry were fascinating. I particularly appreciated the clear and complete explanations of problems from the Egyptian Rhind papyrus and from cuneiform sources.

Not all of the later historical developments are equally worth our time. The sidebars on Viète, Lissajous, and Landau were particularly good, but the ones on Agnesi and De Moivre didn't add much. (This is unfortunate in the case of De Moivre, but I think a sidebar just can't do justice to so great a mathematician--the fun and beauty is lost when you try to squeeze the highlights together.) I agree with Maor that the big names should not be allowed to slide into oblivion, but in a book like this the subject matter should always pass the stricter test of what intrinsic "delights" it offers.

In this genre, the digressive nature of a "journey of discovery" is part of the appeal. But sometimes the thread connecting the episodes was hard to discern here. Chs. 7-8, 10-12 are tedious and feel like padding compared to the well-sustained interest throughout most of the book.

On the other hand, Ch. 14 ("Imaginary Trigonometry") is a masterpiece. With only a basic knowledge of how complex numbers work, readers can appreciate three beautiful examples of conformal mapping (w=sin z, w=e^z, z=w^2). These mappings are chosen and illustrated to your imagination much better than any of the visual exhibits in a standard applied math textbook like Greenberg's "Advanced Engineering Mathematics."

It's in the nature of such a book that sometimes the key problems presented are solved with the help of something that Maor thinks is too advanced or tedious to present to his audience. The result can be that the story of historical progress is obscured by these "rabbit out of a hat" moments. At least, I found that I had to stop and look up the missing pieces, in order to make some of the developments as impressive as they were supposed to be. (I also had to look up some "well-known theorems" in Euclid, read up on the background to Stirling's factorial approximation, etc.)

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.

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.

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!

This book is simply a delight. It explains theorems is a simple cogent manner. The historical content is a bonus. Egyptian clay tablets of right triangles, along with a table, in base 20 no less. Clear writing style, complete and easy to read. Written on a sophomore level, but in an exceedingly well manner.

Discussion and proofs of identities are well written, clear and simple. The double angle formulas for sine and cosine are outstanding.

I purchased three books. One for myself, and two for nephews who were taking trig related subjects.

Eli Maor has other books which are excellent including (paraphrasing) Pi, e, Venus in Transit.
Read Trigonometric Delights as it is a masterpiece. I have two degrees BSEE and MSEE so I know of what I speak. This was a simple and entertaining read for someone who has had a trig course, and is recommended as a supplement book when taking a trig course.

Outstanding!

First, this is not an instructional text and falls into the category of popular math books for the masses.

This is another, history of math with some math in it and a some neat applications. So if you are not a math type, the historical and presentation of the applications makes it a worthwhile read.
If you are a math type, this book still has enough history and some applications that you probably have not read in your trig book. Yes, a good number of the applications are presented in every trig textbook. The author's presentation is alot more exciting than the average trig text, and there are enough of interesting applications which will make it worthwhile.

With the rise of popular math books there are a large number which mix the history and the theorems. But few authors are good at it, and the ones who can do it, are great at it. Maor does an excellent job.

His goal is to make trig engaging. Which is a good thing. considering trig is not even a required course in a good number of high school's cirriculum. When I was in high school you really could not take Calculus without it. Now you can get to college without ever taking trig.

So for a student , it offers a nice incentive to learn trig. Also the historical presentation is always a great resource for understanding math. Textbooks throw this stuff in as sidebars, but they never put it in its historical context. So this genre of book is worthwhile to the student.

For me, trig really became fun when I took a drafting course, and had to apply it. And it was fun. Hopefully this book will make it fun for a student to really learn trig.

bouth it for my husband..just asked what he thinks of it..he said: "I LOVE IT!"

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!

Trigonometry and geometry are important parts for understand or handle what happend with the thigs in our world. Usually you can use these for study a force like a vector in the space, or you will need verify how are related forces several in parts of a complex structure, or you want to discover by yourself how was verified earth shape and who made it first.

Maybe you under siege for an incredible account of information of strange scientifics developments in the past, finally you need understand what is a amazing science, is part of our knowledge. Maybe you think that is too much cold, bored and so useless, but when you read this historical adventure you would say it's incredible, I don't have idea!.

With this kind of book that we can understand our complex knowledge legacy and get more value for it, because this is science not magic, it should be a very usefull tool for teachers and students.