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 geodesics on surfaces, before finally making contact with the idea of shortest paths towards the end of the chapter.
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© 2010 Springer-Verlag London Limited
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Pressley, A. (2010). Geodesics. In: Elementary Differential Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84882-891-9_9
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DOI: https://doi.org/10.1007/978-1-84882-891-9_9
Publisher Name: Springer, London
Print ISBN: 978-1-84882-890-2
Online ISBN: 978-1-84882-891-9
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