Trigonometric Delights

Rating:
Summary: Inspirational!
Review: 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!

Rating:
Summary: The Good Parts Are Good!
Review: 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.)

Rating:
Summary: I don't like Tea
Review: Some people might say: "This book wasn't my cup of tea".I suppose I don't like tea then. Maor's book "may" be interesting to the more historically fixated, but being more interested in math, I found this book too light on proof and theory and more of an anecdotal acounting of the lives of mathematicians. If you're like me, you don't care if the Ambasador of Zanzibar created the double-angle equation, you just want the proof; the proof is lacking, therefore so is the book.(My apologies to the Ambasador of Zanzibar, it isn't my intention to implicate you in any double-angle scandal.) I often secretly read math outlines in history class; this is like reading an outline of history in math class. The font was terrific though!

Rating:
Summary: generous
Review: 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.

Rating:
Summary: Historical Adventure
Review: 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.

Rating:
Summary: Historical Adventure
Review: 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.

Rating:
Summary: Simply Delightful
Review: 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.

Rating:
Summary: Simply Delightful
Review: 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.