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  • Metric expansion of space — Physical cosmology Universe · Big Bang …   Wikipedia

  • Nonlinear dimensionality reduction — High dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies on an embedded non linear manifold within… …   Wikipedia

  • Schwarzschild coordinates — In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres . In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical… …   Wikipedia

  • Slice genus — In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4 ball genus ) is the least integer g such that K is the boundary of a connected, orientable 2 manifold S of genus g embedded in the 4 ball D4… …   Wikipedia

  • Local flatness — In topology, a branch of mathematics, local flatness is a property of a submanifold in a topological manifold of larger dimension. Suppose a d dimensional manifold N is embedded in an n dimensional manifold M (where d lt; n ). If x in N, we say N …   Wikipedia

  • Jordan–Schönflies theorem — In mathematics, the Jordan–Schönflies theorem, or simply the Schönflies theorem, of geometric topology is a sharpening of the Jordan curve theorem.FormulationIt states that not only does every simple closed curve in the plane separate the plane… …   Wikipedia

  • Alexander polynomial — In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a… …   Wikipedia

  • Isotropic coordinates — In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres . There are several different types of coordinate chart which are adapted to this family of nested spheres; the best known is the… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

  • Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

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