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Plane (geometry) print that page


In mathematics , a plane is any flat, two- dimensional surface . A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a space (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or

Plane geometry print that page

In mathematics , plane geometry may refer to: Euclidean plane geometry , the geometry of plane figures, geometry of a plane , or sometimes: geometry of a projective plane , most commonly the real projective plane but possibly the complex projective plane , Fano plane

wikipedia.org | 2011/2/17 23:03:03

Hyperbolic geometry print that page


In mathematics , hyperbolic geometry (also called Lobachevskian geometry or Bolyai -Lobachevskian geometry ) is a non-Euclidean geometry , meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement

Affine plane (incidence geometry) print that page

In incidence geometry , an affine plane is a system of points and lines that satisfy the following axioms ( Cameron 1991 , chapter 2): Any two distinct points lie on a unique line. Given a point and line there is a unique line which contains the point and is parallel to the line There

wikipedia.org | 2011/2/6 3:15:09

Contact (mathematics) print that page

forms are particular differential forms of degree 1 on odd-dimensional manifolds; see contact geometry . Contact transformations are related changes of co-ordinates, of importance in classical mechanics . See also Legendre transformation . Contact between manifolds is often studied in

wikipedia.org | 2011/3/3 1:39:42

Reflection (mathematics) print that page

isometry with a hyperplane as set of fixed points ; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter

wikipedia.org | 2011/4/18 18:43:19

Differential geometry of surfaces print that page


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: extrinsically , relating to their embedding in Euclidean space and intrinsically

Projective space print that page


vector space V . The cases when V = R 2 or V = R 3 are the projective line and the projective plane , respectively. The idea of a projective space relates to perspective , more precisely to the way an eye or a camera projects a 3D scene to a 2D image. All points which lie on a projection

Analytic geometry print that page

In classical mathematics, analytic geometry , also known as coordinate geometry , or Cartesian geometry , is the study of geometry using a coordinate system and the principles of algebra and analysis . This contrasts with the synthetic approach of Euclidean geometry , which treats

wikipedia.org | 2011/10/1 14:31:54

Projective geometry print that page

In mathematics , projective geometry is the study of geometric properties that are invariant under projective transformations . This means that, compared to elementary geometry , projective geometry has a different setting, projective space , and a selective set of basic geometric concepts

wikipedia.org | 2011/5/16 22:53:49