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affine plane

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  • Affine geometry — is a form of geometry featuring the unique parallel line property (see the parallel postulate) but where the notion of angle is undefined and lengths cannot be compared in different directions (that is, Euclid s third and fourth postulates are… …   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

  • Affine group — In mathematics, the affine group or general affine group of any affine space over a field K is the group of all invertible affine transformations from the space into itself.It is a Lie group if K is the real or complex field or… …   Wikipedia

  • Affine differential geometry — Affine differential geometry, as its name suggests, is a type of differential geometry. The basic difference between affine and Riemannian differential geometry is that in the affine case we introduce volume forms over a manifold instead of… …   Wikipedia

  • affine — affine1 [ə fīn′, afīn′] n. a person related by marriage affinal adj. affine2 [ə fīn′, afīn′] adj. [< L affinis: see AFFINITY] Math. of or having to do with projecting or mapping a geometric figure on a second plane or surface so that the new… …   English World dictionary

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

  • Affine space — In mathematics, an affine space is an abstract structure that generalises the affine geometric properties of Euclidean space. In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one… …   Wikipedia

  • Affine transformation — In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis , connected with ) between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation::x… …   Wikipedia

  • Plane at infinity — In projective geometry, the plane at infinity is a projective plane which is added to the affine 3 space in order to give it closure of incidence properties. The result of the addition is the projective 3 space, P^3 . If the affine 3 space is… …   Wikipedia

  • Affine involution — In Euclidean geometry, of special interest are involutions which are linear or affine transformations over the Euclidean space R n . Such involutions are easy to characterize and they can be described geometrically.Linear involutionsTo give a… …   Wikipedia

  • Affine hull — In mathematics, the affine hull of a set S in Euclidean space R n is the smallest affine set containing S , or equivalently, the intersection of all affine sets containing S . Here, an affine set may be defined as the translation of a vector… …   Wikipedia

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