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Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry Hardcover – 23 Dec 2012

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Product details

  • Hardcover: 208 pages
  • Publisher: Princeton University Press (23 Dec. 2012)
  • Language: English
  • ISBN-10: 0691148929
  • ISBN-13: 978-0691148922
  • Product Dimensions: 23.6 x 16 x 2.5 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 361,033 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers.--Alexander Bogomolny "CTK Insights "

Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun.--R. Balashankar "Organiser "

"A beautiful popular book."--"ThatsMaths.com"

Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics

"A beautiful popular book."--
"ThatsMaths.com"




One of "Choice"'s Outstanding Academic Titles for 2013

Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics


"A beautiful popular book."--"ThatsMaths.com"


"The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers."--Alexander Bogomolny, "CTK Insights"

"A no-nonsense introduction to spherical trigonometry."--"Book News, Inc."

"Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun."--R. Balashankar, "Organiser"

""Heavenly Mathematics" is a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. . . . Van Brummelen's book invites readers to consider trigonometry in more than two dimensions, making it a useful supplement to a college geometry or trigonometry class."--"Choice"

""Heavenly Mathematics" proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader."--Florin Diacu, "Literary Review of Canada"

"Glen van Brummelen has written a wonderful introduction to the forgotten subject of spherical trigonometry that draws on the history of the subject to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about. He has succeeded in writing a book that is not intended for historians of science, but which historians of science will find little to complain about and indeed will surely enjoy reading. The book itself is handsomely produced with dozens of attractive illustrations and sold at an affordable price. If spherical trigonometry is ever to become a widely known subject again, this book will surely have played a major role in rescuing it from obscurity."--John M. Steele, "Metascience"

"This book is an excellent survey of spherical trigonometry, discussing and explaining many historic and modern applications in detail and giving full proofs for all theorems. The author has found the right conversational style for a very broad audience, like high school students and teachers of mathematics and amateur historians, who might also skip the proofs. A series of figures from old textbooks and photographs of historical teaching aids make the book very appealing."--Martin Funk, "Mathematical Reviews"

"This is a lovely book to read. I gained a great deal of satisfaction from working through the proofs and constructions, not least because the author has succeeded in convincing me that spherical trigonometry is not as hard as I once thought it was. The style and level of the book are definitely suited to those secondary school pupils who are prepared to follow the technical details, and perhaps try their hand at the very many exercises that are included. More generally, however, the book would provide a wonderful introduction for anyone who wishes to learn more about this subject. Having read the book, I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it."--Christopher Hollings, "Mathematics Today"

"The author's style is engaging, clear, and not overly technical; you can safely lend this book to your friends in the history department. . . . [T]he book is excellent, and would be suited to a wide readership. Libraries (school and university) should give it serious consideration, and it is reasonably priced for private purchase."--Robert Dawson, "Zentralblatt MATH"

""Heavenly Mathematics" will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject."--Jan P. Hogendijk, "Isis"

"This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students."--Teresa Floyd, "Mathematics Teacher"

"Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins. . . . Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative."--P.N. Ruane, "Mathematical Gazette"

"An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics."--Elizabeth Hamm, "Aestimatio Critical Reviews in the History of Science"

One of "Choice"'s Outstanding Academic Titles for 2013
Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics

From the Back Cover

""Heavenly Mathematics" is heavenly, is mathematics, and is so much more: history, astronomy, geography, and navigation replete with historical illustrations, elegant diagrams, and charming anecdotes. I haven't followed mathematical proofs with such delight in decades. If, as the author laments, spherical trigonometry was in danger of extinction, this book will give it a long-lasting reprieve."--David J. Helfand, president of the American Astronomical Society

"This beautifully written book on an unusual topic, with its wealth of historical information about astronomy, navigation, and mathematics, is greatly to be welcomed."--Robin Wilson, president of the British Society for the History of Mathematics, author of "Four Colors Suffice: How the Map Problem Was Solved"

"Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. "Heavenly Mathematics" breathes new and interesting life into a topic that has been slumbering for far too long."--June Barrow-Green, associate editor of "The Princeton Companion to Mathematics"

""Heavenly Mathematics" is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."--Fernando Q. Gouvea, Colby College

"Van Brummelen provides not only a wonderful historical treatment of spherical trigonometry but also a modern one that shows how the ancient and medieval methods were replaced by newer and simpler means of problem solving. Many students will find this a fascinating and worthwhile subject."--Victor J. Katz, editor of "The Mathematics of Egypt, Mesopotamia, China, India, and Islam""

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Students love some of these problems!
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: HASH(0x9f016780) out of 5 stars 20 reviews
53 of 58 people found the following review helpful
HASH(0x9e5bc5b8) out of 5 stars Wonderful Book, but NOT just for history! 24 Dec. 2012
By Let's Compare Options Preptorial - Published on Amazon.com
Format: Hardcover Verified Purchase
The author is so wonderfully entranced and entrancing with this "lost art" that he kindof misses the fact that some of the "old" arts like quaternions (revolving around a world centered on the square root of negative 1 instead of 1!), triangular polygons on surfaces, Napier's pentagon, etc. are being reborn today in the art and craft of modeling, game programming, simulation, digital art and computer graphics (eg. Maya, ZBrush).

Sure, there are now algorithms and calculus functions that "eclipse" the ancient navigational methods, not to mention GPS, but no self respecting GIS teacher can ignore Spherical Trig even today! Wolfram in particular has spent a lot of time tinkering with Java and other applets in spherical trig, and many GIS (Geographical Information Systems) teachers I know will LOVE this text.

This book is really about the beauty of mathematics, and in a Platonic sense, the translation of angular dimensions and fractals into the "real spherical" world not only of planets and stars, but more recently, molecules and RNA folding. If you're a math amateur, you'll love the beauty, and the trig is doable with a little review. If you're a pro, you might just find relationships that newer methods have obscured, but give you many "aha" moments about limits and even hyper modern applications like inverse kinematics, joints and robotics that often have to translate angular into circular momentum and are full of what we'd call trig functions and ODE's today. You'll love this whether you're doing robotics, or working on prosthetic limbs, as well as the more obvious celestial and navigational applications.

"Al-Jabr" (Muḥammad ibn Mûsâ al-Khwârizmî) is often given as the major example of Islamic contributions to math, with less reference to the Spanish Moor salvation of many Greek discoveries Justin tried to destroy, and nearly none to spherical trig. The author reprises these contributions with notes on how the lunar calendar posed problems whose Islamic solutions contributed to far more than the calendar. I'm not Islamic, but it is interesting to see the system presented in a science frame here in the West once in a while.

There are also some very cool and accurate "corrections" to the history of astronomy. As many of you probably know, Kepler was credited with a lot of work actually done by Tycho Brahe, who's area of expertise was, among many others -- you guessed it-- Spherical trig. Although the theory of ST is deep, vast and ancient, applying it, without Maple, was far from easy, and the top math minds of the ancients were baffled by the "tiny" details (read calculus) when one tried to apply theory to the reality of polygon to sphere. Python programmers will smile at this when considering the brute force needed to x/y/z a asteroid pocked sphere in Maya, vs. using code.

All in all, this book is highly recommended. The other reviewers give the glowing historical value, but I wanted to add another facet-- the fact that this art is far from irrelevant to today's most exciting topics in math in addition to the historical beauty and importance. A related field that might interest you as well (search it on Wiki) is Orthographic or Orthogonal Projection. This "old" cartography art also is being reborn in 2D to 3D and vice versa projection in as far ranging fields as biomedical visualization, galaxy modeling and gaming. The Etymology of some of these terms is fascinating, for example, Ortho-doxy translates as "the straight path to glory!" Certainly in the spirit of this volume, with wonder and beauty as important to the author as the math.

I'm a technical consultant, digital artist and mathematician at ShaderJoes dot com and have nothing to do with this book's author, publisher, or Amazon. My review is solely for Amazon shoppers, and we always buy the books we review here.
15 of 17 people found the following review helpful
HASH(0x9e5c71f8) out of 5 stars odd but interesting 2 July 2013
By Henry Spencer - Published on Amazon.com
Format: Hardcover Verified Purchase
This book can't quite decide whether it wants to be a history of the neglected field of spherical trigonometry, or a textbook on it (complete with derivations and problem sets). Fortunately, it succeeds reasonably well at both. If you're more interested in the history, you can just skim lightly over the mathematical details and it still reads well. If you want to learn spherical trig, the history may be a bit of a digression but it's an interesting digression. The later chapters on applications are particularly noteworthy, since few math books nowadays condescend to discuss such mundane matters as how the mathematical methods might get used. An interesting and rewarding book.
14 of 16 people found the following review helpful
HASH(0x9e5c70d8) out of 5 stars Of historical as well as mathematical interest 10 Feb. 2013
By Joseph Hilbe - Published on Amazon.com
Format: Hardcover
A previous review has done a good job on providing an overview of the book. I will not duplicate the effort. I wish to emphasize though that "Heavenly Mathematics" gives the reader a real insight into the background and rationale used by mathematicians of the past in understanding spherical trig. It is one of those rare mathematics books which is difficult to stop reading once started.

The author takss a geometrical approach or focus rather than an algebraic approach to learning spherical trigonometry. Moreover, as indicated earlier, this provides a way of "seeing" the relationships, which aides in remembering them. For anyone wanting to understand this area of mathematics, I highly recommend that read through this volume first.

In addition, professors who teach intoductory to astronomy classes, or observational astronomy, as well as courses on the history of science, should read this book as well. Spherical trigonometry played a vital role in history, being used to locate navigate throughout the world - both on land and at sea.
13 of 16 people found the following review helpful
HASH(0x9e5c60b4) out of 5 stars A welcome relief for a modern mathematician having forgotten about spherical trigonometry 11 Jan. 2013
By Amazon Customer - Published on Amazon.com
Format: Kindle Edition Verified Purchase
A heavenly book for the holidays of a mathematician who sometime desire to have some light matter to read and yet wants to stay "in mathematics". I learned the subject in an introductory lecture on astronomy, and very much regret that 50 years ago that book did not exist!
8 of 10 people found the following review helpful
HASH(0x9e5c6438) out of 5 stars Great book! 10 May 2013
By DCarlisle - Published on Amazon.com
Format: Hardcover Verified Purchase
From a 3rd year math major:
I would definitely recomend this book to anyone interested in learning about spherical geometry, spherical trig, or anyone interested in mathematics generally. It starts with really good background information and progresses fluidly through spherical geometry, then into spherical trig, and practical applications. It is written in a way that if you just want the overview of the material you can get it, but if you really want to dig in there are numerous proofs and an abundance of in depth material as well. It is also nice that the author distinguishes where the detailed explanations are so you can skip over them if you so choose. There are also exercises at the end of each section that challence your knowedge of what you just read and require you to use some creative mathematical skills as well. This could easily be used as a text book on this material. If you take the shorter route, this book can be read through quite quickly and easily, but if you choose to actually study the information and related proofs you can spend quite a bit of time on this material. I read it through completely once, taking time to understand the proofs and examples, and grasped the bulk of the information. I plan to read through it again shortly and try to make sense of the things I couldn't get through the first time. The better your beginning knowledge in Euclidean geometry, algebra, and trigonometry, the more you will gain from this book.
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