Abstract
Geodesics are curves in surfaces that play a role analogous to that of straight lines in the plane. Straight lines in the plane have three important properties:
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(1)
There is a unique straight line containing any two distinct points
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(2)
the straight line between any two points is the shortest path between the points
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(3)
a straight line “does not bend to the left or right as we travel along it.” (This could be restated more precisely by saying that some appropriate derivative is constant.)
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© 1997 Springer Science+Business Media New York
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Bloch, E.D. (1997). Geodesics. In: A First Course in Geometric Topology and Differential Geometry. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8122-7_7
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DOI: https://doi.org/10.1007/978-0-8176-8122-7_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-8121-0
Online ISBN: 978-0-8176-8122-7
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