Karl Jones: /* External links */

2016-04-25T01:25:43Z

‎External links

Karl Jones: /* See also */

2016-02-13T01:21:14Z

‎See also

Karl Jones: Created page with "In differential geometry, a '''geodesic''' (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces"..."

2016-02-13T01:20:38Z

Created page with "In differential geometry, a '''geodesic''' (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces"..."

New page

In [[differential geometry]], a '''geodesic''' (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces".

== Description ==

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.

== Terminology ==

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.

== General relativity ==

Geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of inertial test particles.

== See also ==

* [[Geodesy]]
* [[Mathematics]]

== External links ==

* [https://en.wikipedia.org/wiki/Geodesic Geodesic] @ Wikipedia

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 * [[Geodesy]]
 * [[Mathematics]]
 ==  External links ==
 * [https://en.wikipedia.org/wiki/Geodesic Geodesic] @ Wikipedia

Geodesic - Revision history

Karl Jones: /* External links */

Karl Jones: /* See also */

Karl Jones: Created page with "In differential geometry, a '''geodesic''' (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces"..."