Heavenly Mathematics (ebook)

Argumento de Heavenly Mathematics (ebook)

"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

"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

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

"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. Gouvêa, 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

"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

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

"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 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

"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

"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

"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

"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

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

"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 Science0Preface vii
1 Heavenly Mathematics 1
2 Exploring the Sphere 23
3 The Ancient Approach 42
4 The Medieval Approach 59
5 The Modern Approach: Right- Angled Triangles 73
6 The Modern Approach: Oblique Triangles 94
7 Areas, Angles, and Polyhedra 110
8 Stereographic Projection 129
9 Navigating by the Stars 151
Appendix A. Ptolemy's Determination of the Sun's Position 173
Appendix B. Textbooks 179
Appendix C. Further Reading 182
Index 189