Abstract
Geodesics are the curves in a surface that a bug living in the surface would perceive to be straight. For example, the shortest path between two points in a surface is always a geodesic. We shall actually begin by giving a quite different definition of geodesics, since this definition is easier to work with. We give various methods of finding the geodesics on surfaces, before finally making contact with the idea of shortest paths towards the end of the chapter.
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© 2001 Springer-Verlag London
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Pressley, A. (2001). Geodesics. In: Elementary Differential Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-3696-5_8
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DOI: https://doi.org/10.1007/978-1-4471-3696-5_8
Publisher Name: Springer, London
Print ISBN: 978-1-85233-152-8
Online ISBN: 978-1-4471-3696-5
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