Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

by Glen Van Brummelen


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An unparalleled illustrated history of spherical trigonometry from antiquity to today

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.

Product Details

ISBN-13: 9780691175997
Publisher: Princeton University Press
Publication date: 04/04/2017
Pages: 216
Sales rank: 811,451
Product dimensions: 6.10(w) x 9.20(h) x 0.70(d)

About the Author

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.

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

What People are Saying About This

From the Publisher

"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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