Curvature of a measure — In mathematics, the curvature of a measure defined on the Euclidean plane R2 is a quantification of how much the measure s distribution of mass is curved . It is related to notions of curvature in geometry. In the form presented below, the… … 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
Menger curvature — In mathematics, the Menger curvature of a triple of points in n dimensional Euclidean space Rn is the reciprocal of the radius of the circle that passes through the three points. It is named after the Austrian American mathematician Karl Menger.… … Wikipedia
Fresnel integral — S(x) and C(x) The maximum of C(x) is about 0.977451424. If πt²/2 were used instead of t², then the image would be scaled vertically and horizontally (see below). Fresnel integrals, S(x) and C(x), are two transcendental functions named aft … 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
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
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
Affine curvature — This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection. Special affine curvature, also known as the equi affine curvature or affine curvature, is a particular type of curvature… … Wikipedia
Total curvature — In mathematical study of the differential geometry of curves, the total curvature of a plane curve is the integral of curvature along a curve taken with respect to arclength::int a^b k(s),ds.The total curvature of a closed curve is always an… … Wikipedia
Trigonometric integral — Si(x) (blue) and Ci(x) (green) plotted on the same plot. In mathematics, the trigonometric integrals are a family of integrals which involve trigonometric functions. A number of the basic trigonometric integrals are discussed at the list of… … Wikipedia