Geodesic | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Geodesic


00:01:03 1 Introduction
00:03:56 1.1 Examples
00:04:34 2 Metric geometry
00:06:41 3 Riemannian geometry
00:07:42 3.1 Calculus of variations
00:12:01 4 Affine geodesics
00:13:14 4.1 Existence and uniqueness
00:14:13 4.2 Geodesic flow
00:17:31 4.3 Geodesic spray
00:18:52 4.4 Affine and projective geodesics
00:21:13 5 Computational methods
00:23:39 6 Applications
00:25:38 7 See also
00:25:54 8 References



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SUMMARY
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In differential geometry, a geodesic () is a generalization of the notion of a "straight line"  to "curved spaces". The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle.  The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.
In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. If this connection is the Levi-Civita connection induced by a Riemannian metric, then the geodesics are (locally) the shortest path between points in the space.
Geodesics are of particular importance in general relativity.  Timelike geodesics in general relativity describe the motion of free falling test particles.