Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
"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.
"A beautiful popular book."--ThatsMaths.com
"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
Table of Contents:
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
Another Princeton book authored or coauthored by Glen Van Brummelen: