Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Affine_geometry> ?p ?o }
- Affine_geometry abstract "In mathematics, affine geometry is what remains of Euclidean geometry, when not using (mathematicians often say \"when forgetting\") the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines. Therefore, Playfair's axiom (given a line L and a point P not on L, there is exactly one line parallel to L that passes through P) is fundamental in affine geometry. Comparisons of figures in affine geometry are made with affine transformations, which are mappings that preserve alignment of points and parallelism of lines.Affine geometry can be developed in two ways that are essentially equivalent.In synthetic geometry, an affine space is a set of points to which is associated a set of lines, which satisfy some axioms (such as Playfair's axiom).Affine geometry can also be developed on the basis of linear algebra. In this context an affine space is a set of points equipped with a set of transformations (that is bijective mappings), the translations, which forms a vector space (over a given field, commonly the real numbers), and such that for any given ordered pair of points there is a unique translation sending the first point to the second; the composition of two translations is their sum in the vector space of the translations.In more concrete terms, this amounts to having an operation that associates to any ordered pair of points a vector and another operation that allows translation of a point by a vector to give another point; these operations are required to satisfy a number of axioms (notably that two successive translations have the effect of translation by the sum vector). By choosing any point as \"origin\", the points are in one-to-one correspondence with the vectors, but there is no preferred choice for the origin; thus an affine space may be viewed as obtained from its associated vector space by \"forgetting\" the origin (zero vector).".
- Affine_geometry thumbnail Translation_parallelogram.svg?width=300.
- Affine_geometry wikiPageExternalLink geombchap2.pdf.
- Affine_geometry wikiPageExternalLink pps2.pdf.
- Affine_geometry wikiPageID "243890".
- Affine_geometry wikiPageLength "17864".
- Affine_geometry wikiPageOutDegree "106".
- Affine_geometry wikiPageRevisionID "686235369".
- Affine_geometry wikiPageWikiLink Abelian_group.
- Affine_geometry wikiPageWikiLink Addison-Wesley.
- Affine_geometry wikiPageWikiLink Affine_group.
- Affine_geometry wikiPageWikiLink Affine_plane_(incidence_geometry).
- Affine_geometry wikiPageWikiLink Affine_space.
- Affine_geometry wikiPageWikiLink Affine_transformation.
- Affine_geometry wikiPageWikiLink August_Ferdinand_Möbius.
- Affine_geometry wikiPageWikiLink Axiom.
- Affine_geometry wikiPageWikiLink Barycenter.
- Affine_geometry wikiPageWikiLink Bijection.
- Affine_geometry wikiPageWikiLink Category:Affine_geometry.
- Affine_geometry wikiPageWikiLink Centroid.
- Affine_geometry wikiPageWikiLink Cevas_theorem.
- Affine_geometry wikiPageWikiLink Combinatorics.
- Affine_geometry wikiPageWikiLink Configuration_(geometry).
- Affine_geometry wikiPageWikiLink Congruence_(geometry).
- Affine_geometry wikiPageWikiLink D._Reidel.
- Affine_geometry wikiPageWikiLink David_Hilbert.
- Affine_geometry wikiPageWikiLink Desarguess_theorem.
- Affine_geometry wikiPageWikiLink E._T._Whittaker.
- Affine_geometry wikiPageWikiLink Edwin_Bidwell_Wilson.
- Affine_geometry wikiPageWikiLink Emil_Artin.
- Affine_geometry wikiPageWikiLink Envelope_(mathematics).
- Affine_geometry wikiPageWikiLink Equivalence_relation.
- Affine_geometry wikiPageWikiLink Erlangen_program.
- Affine_geometry wikiPageWikiLink Euclidean_geometry.
- Affine_geometry wikiPageWikiLink Felix_Klein.
- Affine_geometry wikiPageWikiLink Field_(mathematics).
- Affine_geometry wikiPageWikiLink Finite_geometry.
- Affine_geometry wikiPageWikiLink Function_composition.
- Affine_geometry wikiPageWikiLink General_linear_group.
- Affine_geometry wikiPageWikiLink Geometry.
- Affine_geometry wikiPageWikiLink Gilbert_N._Lewis.
- Affine_geometry wikiPageWikiLink Group_(mathematics).
- Affine_geometry wikiPageWikiLink Group_theory.
- Affine_geometry wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Affine_geometry wikiPageWikiLink Hermann_Weyl.
- Affine_geometry wikiPageWikiLink Hyperbolic_orthogonality.
- Affine_geometry wikiPageWikiLink Hyperplane.
- Affine_geometry wikiPageWikiLink Hyperplane_at_infinity.
- Affine_geometry wikiPageWikiLink Introductio_in_analysin_infinitorum.
- Affine_geometry wikiPageWikiLink Isaak_Yaglom.
- Affine_geometry wikiPageWikiLink John_Wiley_&_Sons.
- Affine_geometry wikiPageWikiLink Katsumi_Nomizu.
- Affine_geometry wikiPageWikiLink Leonhard_Euler.
- Affine_geometry wikiPageWikiLink Linear_algebra.
- Affine_geometry wikiPageWikiLink Macmillan_Publishers.
- Affine_geometry wikiPageWikiLink Mathematical_physics.
- Affine_geometry wikiPageWikiLink Mathematics.
- Affine_geometry wikiPageWikiLink Menelaus_theorem.
- Affine_geometry wikiPageWikiLink Metric_(mathematics).
- Affine_geometry wikiPageWikiLink Metric_space.
- Affine_geometry wikiPageWikiLink Minkowski_space.
- Affine_geometry wikiPageWikiLink Moulton_plane.
- Affine_geometry wikiPageWikiLink Non-Desarguesian_plane.
- Affine_geometry wikiPageWikiLink Non-Euclidean_geometry.
- Affine_geometry wikiPageWikiLink Ordered_geometry.
- Affine_geometry wikiPageWikiLink Oswald_Veblen.
- Affine_geometry wikiPageWikiLink Pappus_of_Alexandria.
- Affine_geometry wikiPageWikiLink Parallel_(geometry).
- Affine_geometry wikiPageWikiLink Parallel_postulate.
- Affine_geometry wikiPageWikiLink Parallel_transport.
- Affine_geometry wikiPageWikiLink Parallelepiped.
- Affine_geometry wikiPageWikiLink Perpendicular.
- Affine_geometry wikiPageWikiLink Peter_Cameron_(mathematician).
- Affine_geometry wikiPageWikiLink Playfairs_axiom.
- Affine_geometry wikiPageWikiLink Primitive_notion.
- Affine_geometry wikiPageWikiLink Projective_geometry.
- Affine_geometry wikiPageWikiLink Projective_space.
- Affine_geometry wikiPageWikiLink Real_number.
- Affine_geometry wikiPageWikiLink Rotation_(mathematics).
- Affine_geometry wikiPageWikiLink Russian_language.
- Affine_geometry wikiPageWikiLink Scripta_Mathematica.
- Affine_geometry wikiPageWikiLink Semidirect_product.
- Affine_geometry wikiPageWikiLink Special_relativity.
- Affine_geometry wikiPageWikiLink Squeeze_mapping.
- Affine_geometry wikiPageWikiLink Symmetry.
- Affine_geometry wikiPageWikiLink Synthetic_geometry.
- Affine_geometry wikiPageWikiLink Transformation_geometry.
- Affine_geometry wikiPageWikiLink Translation_(geometry).
- Affine_geometry wikiPageWikiLink University_of_London.
- Affine_geometry wikiPageWikiLink University_of_Pennsylvania.
- Affine_geometry wikiPageWikiLink University_of_Toronto_Press.
- Affine_geometry wikiPageWikiLink Vector_space.
- Affine_geometry wikiPageWikiLink World_line.
- Affine_geometry wikiPageWikiLink File:PappusAffine.svg.
- Affine_geometry wikiPageWikiLink File:Translation_parallelogram.svg.
- Affine_geometry wikiPageWikiLinkText "Affine geometry".
- Affine_geometry wikiPageWikiLinkText "affine ''d''-space".
- Affine_geometry wikiPageWikiLinkText "affine geometries".
- Affine_geometry wikiPageWikiLinkText "affine geometry".
- Affine_geometry wikiPageWikiLinkText "affine plane".