Trigonometric Delights by Eli Maor (PDF)

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.

User’s Reviews

Editorial Reviews: 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 Review “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 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”[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 ofThe 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 ofMathematics: The Science of Patterns and Goodbye Descartes About the Author Eli Maor teaches the history of mathematics at Loyola University in Chicago. He has published extensively in journals of mathematics and mathematics education and is the author of To Infinity and Beyond , e: The Story of a Number, and June 8, 2004–Venus in Transit (all Princeton). Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐First of all, the book is fantastic. There is no question about that.I own a paper copy, but I wanted a copy on my Kindle, too, so I bought it. Unfortunately, the Kindle version is basically just a photograph of each page of the hard copy. I’m sure that this is basically due to the diagrams and math notation in the book, but it’s something you should know before you buy.You can zoom in on a page to make the print larger, but you can’t re-size text, highlight passages, or look up definitions of words, as you can with a typical Kindle book. You also can’t search the text or touch a footnote number and hyper link to the actual footnote.There is nothing in the descriptive information that indicates this, and there should be. I’m not saying don’t buy it, but I just want people to know what they’re getting.The website makes it look like you can read it in the Kindle Cloud Reader (where I do most of my reading) but that is not the case. It can be read in the app, but not the cloud reader.

⭐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.

⭐My hardcover copy (1998) remains a staple of my mathematics education. My initial reading of this book occurred in 1998 (at which time I was teaching in a “mathematics lab,” which Maor refers to as a college remedial program– preface ). I recently re-read the book and it remains inspiring. Apparently, at the time, educational instruction in trigonometry and geometry were in a state of decline (I had taken those topics in high-school, so I was not absent their appreciation.) Blame for the decline is sometimes placed on “new math.” Maor: “new math did more harm than good.” (I disagree). Read one early trigonometry text and see where things go wrong: “Trigonometry consists largely of formulae.” (1912, Loney).(1) An appendix, entitled “let’s revive an old idea,” is my favorite part of this book. Those pages should be included in a mathematics education (but again, a downplay of the ‘new math.’). You learn trigonometric functions as “projections.” (page 213-217). As collateral, find: Trigonometric Functions, A Problem-Solving Approach (1986, Mir publishers, Panchishkin, page22, available as PDF on Archive).(2) Geometric progression occurs early (page 11) and later (chapter nine, page 122). About which, learn a geometric interpretation of geometric series. Maor: “every trigonometric formula ultimately derives from geometry.” (page 114) and “every trigonometric identity can be interpreted geometrically.” (page 142).Read of the “trigonometric manifestation of the theorem that an angle inscribed in a circle has the same measure as one-half the central angle subtending the same arc, repeated again and again…” (page 143).(3) Revisit applicable elementary mathematics: solving cubic polynomial equation (page 59), parametric equations (page 95), using simple derivative algorithms (quotient rule, page 130), recall limits (page 143), arithmetic and geometric means (pages 47 and 153, neglected often), partial fraction decomposition (page 157, too often neglected).(4) More involved is the elucidation of power series expansions (page 156) and infinite products.Calculus students get much exposure to power series. Less often are they exposed to infinite products.In any event, if you are looking for an entre, they occur early (page 50) and often here.(5) I highlight three chapters: six, ten and twelve. Chapter six expounds on two theorems from geometry: “we will have numerous occasions to use it throughout the book.” (page 87). Chapter ten recalls the limit of the quotient: f(x) = sin (x)/ x. Chapter twelve is entitled tan x (that title sums it up): “perhaps the most remarkable is the tangent function.” (page 150). Simmons textbook of Calculus is quoted (regards Euler).(6) An appendix showing integration of Secant function is lucid (the reader will need to fill in many of the elementary steps in the derivation). Another appendix, Trigonometric Gems, compels you to see Jolley’s book: Summation of Series (1961, Dover publications). Now, read: “The history of mathematics is full of attempts to break the barrier of the impossible.” and “strangeness is a relative concept.” (pages 181, 190).(7) Concluding: Another fine Princeton University Press publication in the mode of inspiring mathematical expositions (see more from Maor, Dunham, Ash and Gross). Dolciani’s elementary textbook series is still worth perusing: Modern Algebra and Trigonometry, Structure and Method. Then, get a copy of Gelfand’s Trigonometry (2001, Birkhauser).

⭐Love books in this series, enjoy reading about topics taht inteterest me.

⭐Tasty little book. Eli Maor has a narrative and mathematical style that lends well to the material.

⭐I purchased this book for my husband, who holds a master’s degree in Math. He loves it. I recommend it.

⭐Mi attendevo dei bei problemi trigonometrici, invece si tratta di un excursus sulla nascita e lo sviluppo storico della trigonometria. Interessante, ma il titolo è fuorviante.

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⭐lovely book

⭐内容的には非常に興味深く面白い本だと思う。数式のすべてを理解するには、数学知識は高校の微積分と三角関数、それに高校３年〜大学教養課程英語レベルぐらいだと思う。英語で読んだ理由は、翻訳(青土社発行｢素晴らしい三角法の世界」の日本語訳がむちゃくちゃなものであるため。本書は三角関数に関しての話題を集め、それをなるべく系統的に説明解説した読み物。数学的にある程度は証明をきちんと入れてはいるが、教科書的に厳格ではない。数学が好きな方が読むときはその部分を自ら証明しながら読んでいくと楽しい。ただ、かなり数式の記載に誤植があるので、おかしいと思ったら徹底的にきちんと証明してみるとよい。Ｋｉｎｄｌｅでこの本を読む場合の長所は、辞書(英語)が簡単に引けること。その他持ち運びとか、読み終わった後の本の置き場所などのＫｉｎｄｌｅならではの長所は当然ある。短所は、この本に限ったことなのかもしれないが、(１)図表と一部の数式が拡大できない。あまりに小さすぎて図表の中の文字が読めない場合や、図表として書かれた数式がある。例えば、＝と≒を見分けることは式の意味を考えない限り不可能。(２)確かに図表を示す「Ｆｉｇ.・・」という部分をタップすれば図表が画面に現れるが、その後本文に戻るときの操作が２回タップというのは煩わしい。また本文と図表は同時に読めないのが不便。(３)ページ数表示がない。代わりに「Ｎｏ・・・・」という４桁の数字があるが、本文中に「see P51」（ｐ５１参照）と書かれている時は探しようがないのは不便。結論として、・数学が趣味の方にとっては、面白く、よい本である。(☆４〜５)・キンドルではお勧めできない。(マイナス☆１〜２つ)・日本語訳はお金を捨てるつもりでない限り買わない方がよい。・ペーパーバックの原書を購入する事をお勧めする。

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