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This article is about lines in mathematics. For Long Interspersed Nuclear Elements in DNA, see Retrotransposon#LINEs. It has been suggested that this article or section be merged with invariant interval. (Discuss) Proposed since December 2010. This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) This article needs attention from an expert on the subject. See the talk page for details. WikiProject Mathematics or the Mathematics Portal may be able to help recruit an expert. (November 2008) A line element ds (alternatively, infinitesimal element of length) in mathematics can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parametrizing the given curve by Frenet's formulas. As such, a line element is then naturally a function of the metric, and can be related to the curvature tensor. The most well known line elements are those of cartesian planar and spatial coordinates. They are given by planar:ds2 = dx2 + dy2 spatial:ds2 = dx2 + dy2 + dz2 Other line elements are given by: flat polar: spherical polar: cylindrical polar: The most general 2- dimensional (coordinates (χ,ψ)) metric is given by Line elements in physics Line elements are used in physics, especially in theories of gravitation such as general relativity, where spacetime is modelled as a curved manifold with a metric. See also First fundamental form Metric tensor This mathematics-related article is a stub. You can help Wikipedia by expanding it.v · d · e This relativity-related article is a stub. You can help Wikipedia by expanding it.v · d · e