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Heavenly MathematicsThe Forgotten Art of Spherical Trigonometry$
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Glen Van Brummelen

Print publication date: 2017

Print ISBN-13: 9780691175997

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175997.001.0001

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Exploring the Sphere

Exploring the Sphere

(p.23) 2 Exploring the Sphere
Heavenly Mathematics

Glen Van Brummelen

Princeton University Press

This chapter introduces the reader to the celestial sphere, or the Earth's surface. By rotating the sphere, the motions of the heavens can be simulated. There are three features of celestial motion that came to be associated with Aristotle: all objects move in circles; they travel at constant speeds on those circles; the Earth is at the center of the celestial sphere. The chapter shows how the movements of stars and planets on the sphere's surface can be determined by setting up a system of equatorial coordinates. It also explains how the celestial sphere can be set in motion through the day, and how Hipparchus of Rhodes endeavored to determine the eccentricity of the Sun's orbit. Finally, it discusses spherical geometry, with emphasis on finding bounds on the sides and angles of a spherical triangle.

Keywords:   celestial sphere, Earth, celestial motion, stars, planets, equatorial coordinates, Hipparchus of Rhodes, Sun, spherical geometry, spherical triangle

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