Cover image for Heavenly mathematics : the forgotten art of spherical trigonometry
Heavenly mathematics : the forgotten art of spherical trigonometry
Van Brummelen, Glen.
Personal Author:
Publication Information:
Princeton ; Oxford : Princeton University Press, [2013]

Physical Description:
xvi, 192 pages, 8 unnumbered pages color plates : illustrations (some color), maps ; 25 cm
Heavenly mathematics -- Exploring the sphere -- The ancient approach -- The medieval approach -- The modern approach: right-angled triangles -- The modern approach: oblique triangles -- Areas, angles, and polyhedra -- Stereographic projection -- Navigation.
Format :


Call Number
Material Type
Home Location
Central Library QA535 .V36 2013 Adult Non-Fiction Non-Fiction Area

On Order



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.

Author Notes

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.

Reviews 1

Choice Review

Heavenly Mathematics is a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. The typical undergraduate curriculum will only hint at this discipline via non-Euclidean geometry. Here, Van Brummelen (Quest Univ. Canada; The Mathematics of the Heavens and the Earth, CH, Aug'09, 46-6864) demonstrates how central the subject was to generations of navigators and geographers. Earth is roughly spherical, and the stars and planets appear to be constrained on a sphere to earthbound observers. Spherical trigonometry allows scientists/mathematicians to calculate positions and distances on the Earth and the heavens. As readers discover this discipline, they will also appreciate the beauty inherent in the topic. The book itself is well written with ample diagrams, photographs, and equations as well as reproductions/plates related to historical spherical trigonometry. The modern mathematics curriculum restricts students, except those at the upper levels, to a two-dimensional plane. As a result, students struggle when asked to transition to three dimensions. Van Brummelen's book invites readers to consider trigonometry in more than two dimensions, making it a useful supplement to a college geometry or trigonometry class. Summing Up: Highly recommended. All levels/libraries. J. T. Noonan Mount Vernon Nazarene University

Table of Contents

Prefacep. vii
1 Heavenly Mathematicsp. 1
2 Exploring the Spherep. 23
3 The Ancient Approachp. 42
4 The Medieval Approachp. 59
5 The Modern Approach: Right-Angled Trianglesp. 73
6 The Modern Approach: Oblique Trianglesp. 94
7 Areas, Angles, and Polyhedrap. 110
8 Stereographic Projectionp. 129
9 Navigating by the Starsp. 151
Appendix A Ptolemy's Determination of the Sun's Positionp. 173
Appendix B Textbooksp. 179
Appendix C Further Readingp. 182
Indexp. 189

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