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Title: Trigonometric Delights
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Manufacturer: Princeton University Press
List Price: $23.95
Our Price: $12.50
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| Customer Reviews: |
| Trigonometric Delights by Princeton University Press Wish They Had 10 Star Ratings! | 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! | | Trigonometric Delights by Princeton University Press Off On A Good Tangent | 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. | | Trigonometric Delights by Princeton University Press anything but a delight | | I was hoping for things I could use in math class but I didn't find anything. | | Trigonometric Delights by Princeton University Press I don't like Tea | | 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! | | Trigonometric Delights by Princeton University Press The Good Parts Are Good! | 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.) | | Trigonometric Delights by Princeton University Press Product Description | 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. |
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