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Trigonometry has always been an underappreciated branch 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: #874536 in eBooks
- Published on: 2013-03-13
- Released on: 2013-03-13
- Format: Kindle eBook
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
"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, MAA Online
"Maor clearly has a great love of trigonometry, formulas and all, and his enthusiasm shines through. . . . If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."--Ian Stewart, New Scientist
"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
From the Inside Flap
"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
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
"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] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, Mathematical Association of America
"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
Most helpful customer reviews
28 of 29 people found the following review helpful.
The Good Parts Are Good!
By T. W.
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.)
2 of 2 people found the following review helpful.
Excellent, something for everyone, both students and average person
By Marc
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 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.
11 of 15 people found the following review helpful.
An ideal book for high school mathematics teachers
By Jordan Bell
Trigonometry is the study of relations between angles and lengths. Indeed SOH CAH TOA and trigonometric identities are part of the subject, but there is much more to the subject than what you may have learned in high school. If you have trouble remembering whether sin(0)=0 or cos(0)=0, you can fix this either by using your calculator to find that sin(0)=0, or you can memorize sin(0)=0 (which at least stores something in your brain, and if the memorization is done severely enough it will indeed last your life), or finally by having such a comprehensive understanding of trigonometry that mixing up sin(0)=0 and cos(0)=0 would be like forgetting whether sugar or salt tastes sweet.
Learning the history of a subject along with learning the content of the subject itself helps you remember material and makes the material feel alive. It also helps with pacing the rate at which you absorb careful mathematical proofs. After reading even a page or two of a serious proof you need time to let the material settle before going on to the next proof. Many in the discipline of mathematics today think of theorems and proofs as real mathematics and anything else as motivation that one should learn to do without. This is wrong; things are true whether or not someone has written them down and things will wait for us to find them out. Anything that helps people absorb mathematics into their brains is real mathematics. (Thus using a calculator to calculate values of trigonometric functions is a skill but not a mathematical skill as it doesn't involve putting mathematics in your brain, any more than idly chatting while playing a video game is practice in public speaking.) Of course talking about the provenance of the Rhind Papyrus has no mathematical content. But it is fun to read about, and it gives you hooks in your mind to remember things about the papyrus. Likewise, learning the etymology of mathematical terms such as sine and degree gives us more ways to summon mathematics from our memory.
This is not a serious work of history like the works of T. L. Heath, D. T. Whiteside, D. H. Fowler, W. K. Bühler, J. E. Hofmann, André Weil, Lucio Russo or Clifford Truesdell, and a careful writer should not use this as a reference. But it is a fun book that shows the reader many different theorems in trigonometry they may not have seen before, and gives the reader an outline of the history of the subject that can be filled in by reading more detailed books.
If you just skim this book, I encourage you to at least read the chapter on Regiomantanus, which presents a problem posed by him: "At what point on the ground does a perpendicularly suspended rod appear largest?" Aside from being a question that doesn't seem contrived, it can involve the arithmetic mean-geometric mean inequality and calculus.
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