Google full text of our books:


Heavenly Mathematics:
The Forgotten Art of Spherical Trigonometry
Glen Van Brummelen

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

Paperback | 2017 | $19.95 | £14.95 | ISBN: 9780691175997
208 pp. | 6 x 9 1/4 | 11 color plates. 30 halftones. 93 line illus.
Hardcover | 2012 | $42.00 | £34.95 | ISBN: 9780691148922
208 pp. | 6 x 9 1/4 | 11 color plates. 30 halftones. 93 line illus. 1 table.
Add to Shopping Cart

eBook | ISBN: 9781400844807 |
Our eBook editions are available from these online vendors

Reviews | Table of Contents
Chapter 1[PDF] pdf-icon

Google full text of this book:

Solutions Manual

Heavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950s. 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 of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

Glen Van Brummelen is coordinator of mathematics at Quest University Canada and former president of the Canadian Society for History and Philosophy of Mathematics. He won the 2016 Haimo Award for Distinguished College or University Teaching of Mathematics, awarded by the Mathematical Association of America, and the 2017 3M National Teaching Fellowship, awarded by the Society for Teaching and Learning in Higher Education.


"Once a mainstay of mathematics, spherical trigonometry no longer appears on school curricula. Here, Glen Van Brummelen reasserts the field's importance, sharing in illuminating detail how it figured in astronomy, cartography and our understanding of Earth's rotation."--Rosalind Metcalfe, Nature

"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."

"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 Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. . . . As readers discover this discipline, they will also appreciate the beauty inherent in the topic."--Choice

More reviews

Table of Contents:

Preface 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

Another Princeton book authored or coauthored by Glen Van Brummelen:

Subject Areas:


Shopping Cart options:

  • For ebooks:

Our eBook editions are available
from these online vendors:

  • Amazon Kindle Store
  • Apple iBooks
  • Barnes & Noble Nook Store
  • Google Play eBook Store
  • Kobo eBook Store
  • Many of our ebooks are available through
    library electronic resources including these platforms:

  • Books at JSTOR
  • Ebrary
  • Ebook Library
  • EBSCO Ebooks
  • MyiLibrary
  • Dawsonera (UK)

    • For hardcover/paperback orders in United States, Canada, Latin America, Asia, and Australia

     Paperback : $19.95 ISBN: 9780691175997

    Add to shopping cart

     Hardcover : $42.00 ISBN: 9780691148922

    Add to shopping cart
    View contents of your shopping cart

    • For hardcover/paperback orders in Europe, Africa, the Middle East, India, and Pakistan

     Hardcover  £34.95 ISBN: 9780691148922

    Add to shopping cart

     Paperback  £14.95 ISBN: 9780691175997

    Add to shopping cart
    View contents of your shopping cart

    Prices subject to change without notice

    File created: 7/11/2017

    Questions and comments to:
    Princeton University Press

    New Book E-mails
    New In Print
    PUP Blog
    Princeton APPS
    Sample Chapters
    Princeton Legacy Library
    Exam/Desk Copy
    Recent Awards
    Princeton Shorts
    Freshman Reading
    PUP Europe
    About Us
    Contact Us
    PUP Home

    Bookmark and Share 
    Send me emails
    about new books in:
    History Of Science And Medicine, Philosophy Of Science
    Astronomy And Cosmology
    More Choices