Trigonometric Delights

by Eli Maor

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.

Genres: Mathematics, Nonfiction, History, Science, Textbooks, Teaching

256 pages, Paperback

First published January 1, 1998

Reviews

[William · Rating 4 out of 5]

A nice refresher of my basic Trig, mixed with some interesting new concepts and historical backgrounds of several important mathematicians. My only complaint is the formatting of the book: many of the diagrams were placed on a page not viewable to where the explanations took place. This made it harder to follow, and resulted in a tendency to skim rather than study. But still, something I'd like to play more with in my spare time.

[Maurizio Codogno · Rating 4 out of 5]

curiosità trigonometriche

Maor lo dice subito: per lui la trigonometria è bellissima, e non si capacita che oramai non venga più insegnata a scuola, con la flebile scusa che con le calcolatrici non serve più avere sistemi per semplificare i conti da fare. Continuo ad avere dubbi sulla bellezza delle trigonometria, ma sono stati scossi un po' da questo testo, che nella prima parte fa una carrellata storica ma nella seconda mostra come tante altre nozioni matematiche che riteniamo ancora oggi utili hanno una correlazione con la trigonometria. Una chicca secondo me è vederla nella proiezione di Mercatore e scoprire che la sua carta geografica non è una proiezione cilindrica come pensano in tanti...
Nota: la versione elettronica del libro è fondamentalmente un PDF, il che significa che o la leggete su un tablet da 10 pollici o su un PC, ma non certo sul furbofono o sul Kindle.

[Wing · Rating 5 out of 5]

It’s an amazing achievement that Maor manages to write an engaging history of the development of trigonometry and its expansion into other branches of mathematics and at the same time explain key concepts clearly and succinctly with most of the mathematics included within dumbing anything down. He also explores some beautiful but often forgotten results. His curation is unavoidably subjective but the result is awe inspiring and intellectually satisfying. Many snippets of the lives of great mathematicians are included, providing frequently needed interludes for the reader to relax a bit before summoning their mind to comprehend complex mathematics again. While his exposition is easy to follow, it does demand prior knowledge of various mathematical subjects for the reader to truly appreciate all its intricacies. I am a medical doctor by trade and trigonometric identities and integration techniques (both are assumed knowledge) only ring a faint bell. Nevertheless, I can follow essentially the whole book (with the exception of perhaps a handful of sentences/assertions). These by no means reduce my enjoyment of reading it. Five stars, and its expansion into other branches of mathematics while simultaneously explaining key concepts clearly and succinctly, with most of the mathematics included without dumbing anything down. He also explores many beautiful but often overlooked results. His curation is inevitably subjective, but the result is awe-inspiring and intellectually satisfying.
The book is enriched by numerous vignettes from the lives of great mathematicians, providing welcome interludes that allow the reader to relax before once again engaging with more demanding mathematics. Although Maor's exposition is easy to follow, it does require prior knowledge of various mathematical subjects for the reader to fully appreciate all of its intricacies. I am a medical doctor by trade, and trigonometric identities and integration techniques—both assumed knowledge—only ring a faint bell for me. Nevertheless, I was able to follow essentially the entire book, with the exception of perhaps a handful of sentences or assertions. These did not diminish my enjoyment in the slightest.
Five stars.

[Tom Concannon · Rating 5 out of 5]

I knew this book was rather “heavy” on the math for a popular level treatise on trigonometry, so I needed to set aside a good chunk of unobstructed time to go through it. After doing so, I was not disappointed! I will use many of the derivations and interesting facts from this book in my future mathematics classes, to not only keep the students on their toes, but to show them how cool trigonometry really is!

[Cristian Sandu · Rating 5 out of 5]

The mix of math and history was interesting and the engaging stories from the past really made me understand the evolution of trigonometry. The author's passion really shines within the pages and it was a pleasant reading for me.

[Nada Khaled · Rating 5 out of 5]

A perfect Trigonometry History

[Carter Dugan · Rating 4 out of 5]

Fun read that assumes some background knowledge. If you like the history of sciences, this is a fun one for the era of "math before calculus".

[Ann · Rating 4 out of 5]

Maor does it again in this fascinating collection of essays on trigonometry. The essays are a combination of history, biographical vignettes, proofs and applications ranging from Pythagoras to map projections to Fourier who avoided geometry like the Plague. Maor presents the basic trigonometric functions, cosine and sine in the historical development of their uses from concrete geometry to more abstract number theory, a far cry from the introduction many had in high school. Despite the attention needed to follow the proofs, this is a delightful book and the proofs are well worth the effort. Highly recommended for math tourists and those interested in intellectual history.

[Jef · Rating 5 out of 5]

Lots of back story and neat proofs. Really suplamemts a course in trigonometry.

[Andrew Davis · Rating 2 out of 5]

A bit disappointing. Too much history and not enough trigonometry.

[E.]

a bit over my head, at least for the level of attention I can give right now. looks good though