Abstract
In this chapter, we study spherical geometry. In order to emphasize the duality between spherical and hyperbolic geometries, a parallel development of hyperbolic geometry will be given in Chapter 3. In many cases, the arguments will be the same except for minor changes. As spherical geometry is much easier to understand, it is advantageous to first study spherical geometry before taking up hyperbolic geometry. We begin by studying spherical n-space. Elliptic n-space is considered in Section 2.2. Spherical arc length and volume are studied in Sections 2.3 and 2.4. The chapter ends with a section on spherical trigonometry.
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© 2006 Springer Science+Business Media, LLC
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(2006). Spherical Geometry. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-47322-2_2
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DOI: https://doi.org/10.1007/978-0-387-47322-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33197-3
Online ISBN: 978-0-387-47322-2
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