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Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

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Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry Cover

 

Synopses & Reviews

Publisher Comments:

"Heavenly Mathematics is heavenly, is mathematics, and is so much more: history, astronomy, geography, and navigation replete with historical illustrations, elegant diagrams, and charming anecdotes. I haven't followed mathematical proofs with such delight in decades. If, as the author laments, spherical trigonometry was in danger of extinction, this book will give it a long-lasting reprieve."--David J. Helfand, president of the American Astronomical Society

"This beautifully written book on an unusual topic, with its wealth of historical information about astronomy, navigation, and mathematics, is greatly to be welcomed."--Robin Wilson, president of the British Society for the History of Mathematics, author of Four Colors Suffice: How the Map Problem Was Solved

"Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. Heavenly Mathematics breathes new and interesting life into a topic that has been slumbering for far too long."--June Barrow-Green, associate editor of The Princeton Companion to Mathematics

"Heavenly Mathematics is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."--Fernando Q. Gouvêa, Colby College

"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

Synopsis:

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.

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

Product Details

ISBN:
9780691148922
Author:
Van Brummelen, Glen
Publisher:
Princeton University Press
Author:
Brummelen, Glen Van
Subject:
History
Subject:
Political Science and International Relations
Subject:
Mathematics
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Astronomy and Cosmology
Subject:
Astronomy - General
Copyright:
Publication Date:
20121231
Binding:
HARDCOVER
Language:
English
Illustrations:
11 color plates. 30 halftones. 93 line i
Pages:
208
Dimensions:
9 x 6 in

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Related Subjects


Science and Mathematics » Astronomy » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » History
Transportation » General

Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry New Hardcover
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$42.50 In Stock
Product details 208 pages Princeton University Press - English 9780691148922 Reviews:
"Synopsis" by ,

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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