Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

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Princeton University Press, 2013 - Mathematics - 192 pages
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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.


 

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Contents

1 Heavenly Mathematics
1
2 Exploring the Sphere
23
3 The Ancient Approach
42
4 The Medieval Approach
59
RightAngled Triangles
73
Oblique Triangles
94
7 Areas Angles and Polyhedra
110
8 Stereographic Projection
129
9 Navigating by the Stars
151
Appendix A Ptolemys Determination of the Suns Position
173
Appendix B Textbooks
179
Appendix C Further Reading
182
Index
189
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About the author (2013)

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.

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