Gaussian surface curvature

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• 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

• Gaussian curvature — In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ 1 and κ 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how… …   Wikipedia

• Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

• curvature — /kerr veuh cheuhr, choor /, n. 1. the act of curving or the state of being curved. 2. a curved condition, often abnormal: curvature of the spine. 3. the degree of curving of a line or surface. 4. Geom. a. (at a point on a curve) the derivative of …   Universalium

• Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …   Wikipedia

• gaussian curvature — sēən noun or gauss curvature Usage: usually capitalized G Etymology: K. F. Gauss died 1855 + English ian : the reciprocal of the product of the two principal radii of curvature of a surface at any of its points …   Useful english dictionary

• Parametric surface — A parametric surface is a surface in the Euclidean space R3 which is defined by a parametric equation with two parameters. Parametric representation is the most general way to specify a surface. Surfaces that occur in two of the main theorems of… …   Wikipedia

• Principal curvature — Saddle surface with normal planes in directions of principal curvatures In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface… …   Wikipedia

• Radius of curvature (applications) — The distance from the center of a sphere or ellipsoid to its surface is its radius. The equivalent surface radius that is described by radial distances at points along the body s surface is its radius of curvature (more formally, the radius of… …   Wikipedia

• Mean curvature — In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The… …   Wikipedia

• Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… …   Wikipedia