Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

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

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 photographs 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.

Product Details

ISBN-13: 9780691148922
Publisher: Princeton University Press
Publication date: 12/23/2012
Pages: 216
Product dimensions: 6.20(w) x 9.30(h) x 1.00(d)

About the Author

Glen Van Brummelen is coordinator of mathematics and the physical sciences at Quest University Canada and president of the Canadian Society for History and Philosophy of Mathematics. His books include "The Mathematics of the Heavens and the Earth: The Early History of Trigonometry" (Princeton) and "Mathematics and the Historian's Craft".

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

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