All about Geodesic. This is another Text 2 Audio transformation using Flite. Below is the transcript for the recording: [[File:Spherical triangle.svg|thumb|right|150px|A geodesic triangle on the sphere. The geodesics are great circle arcs.]] In mathematics, particularly differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". 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 the shortest path between points in the space. 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. Geodesics are of particular importance in general relativity. Geodesics in general relativity describe the motion of inertial test particles.

• published: 08 Oct 2013
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