Abstract
The simplest example of a curved surface is the ordinary 2-dimensional sphere in Euclidean 3-space. Furthermore the geometry of the sphere serves a major motivation for much of the mathematical work that has been done for more general surfaces. For this reason it is useful to examine some basic results associated with the geometry of a sphere.
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- 1.
Most mathematicians will cringe at this definition with good reason. When one travels by plane from New York to London by a great circle route over the Atlantic Ocean, one is following a geodesic. However if one continues over the same great circle, one is still following a geodesic even though it is not the shortest route from London to New York. Nevertheless, I will rely on your intuition and your common sense until I have developed enough mathematical machinery to give a more sophisticated definition in Sect. 5.4 of this chapter.
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Snygg, J. (2012). Curved Spaces. In: A New Approach to Differential Geometry using Clifford's Geometric Algebra. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8283-5_5
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DOI: https://doi.org/10.1007/978-0-8176-8283-5_5
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Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-8282-8
Online ISBN: 978-0-8176-8283-5
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