Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Erlangen_program> ?p ?o }
- Erlangen_program abstract "The Erlangen program is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as Vergleichende Betrachtungen über neuere geometrische Forschungen. It is named after the University Erlangen-Nürnberg, where Klein worked.By 1872, non-Euclidean geometries had emerged, but without a way to determine their hierarchy and relationships. Klein's method was fundamentally innovative in three ways: Projective geometry was emphasized as the unifying frame for all other geometries considered by him. In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry. Klein proposed that group theory, a branch of mathematics that uses algebraic methods to abstract the idea of symmetry, was the most useful way of organizing geometrical knowledge; at the time it had already been introduced into the theory of equations in the form of Galois theory. Klein made much more explicit the idea that each geometrical language had its own, appropriate concepts, thus for example projective geometry rightly talked about conic sections, but not about circles or angles because those notions were not invariant under projective transformations (something familiar in geometrical perspective). The way the multiple languages of geometry then came back together could be explained by the way subgroups of a symmetry group related to each other.Later, Élie Cartan generalized Klein's homogeneous model spaces to Cartan connections on certain principal bundles, which generalized Riemannian geometry.".
- Erlangen_program wikiPageExternalLink 0807.3161..
- Erlangen_program wikiPageExternalLink erlangen.
- Erlangen_program wikiPageExternalLink text-idx?c=umhistmath;idno=ABN7632.
- Erlangen_program wikiPageExternalLink ErlangerProgramm.htm.
- Erlangen_program wikiPageID "243382".
- Erlangen_program wikiPageLength "13452".
- Erlangen_program wikiPageOutDegree "121".
- Erlangen_program wikiPageRevisionID "674311617".
- Erlangen_program wikiPageWikiLink CFT.
- Erlangen_program wikiPageWikiLink CFT_correspondence.
- Erlangen_program wikiPageWikiLink Affine_geometry.
- Erlangen_program wikiPageWikiLink Affine_group.
- Erlangen_program wikiPageWikiLink Alfred_Tarski.
- Erlangen_program wikiPageWikiLink Angle.
- Erlangen_program wikiPageWikiLink Anti-de_Sitter_space.
- Erlangen_program wikiPageWikiLink Arthur_Cayley.
- Erlangen_program wikiPageWikiLink August_Ferdinand_Möbius.
- Erlangen_program wikiPageWikiLink Automorphism.
- Erlangen_program wikiPageWikiLink Automorphism_group.
- Erlangen_program wikiPageWikiLink Bourbaki.
- Erlangen_program wikiPageWikiLink Cartan_connection.
- Erlangen_program wikiPageWikiLink Category:Classical_geometry.
- Erlangen_program wikiPageWikiLink Category:Erlangen.
- Erlangen_program wikiPageWikiLink Category:Group_theory.
- Erlangen_program wikiPageWikiLink Category:Homogeneous_spaces.
- Erlangen_program wikiPageWikiLink Category:Symmetry.
- Erlangen_program wikiPageWikiLink Category_theory.
- Erlangen_program wikiPageWikiLink Charles_Ehresmann.
- Erlangen_program wikiPageWikiLink Circle.
- Erlangen_program wikiPageWikiLink Classical_group.
- Erlangen_program wikiPageWikiLink Classical_groups.
- Erlangen_program wikiPageWikiLink Conformal_geometry.
- Erlangen_program wikiPageWikiLink Conformal_space.
- Erlangen_program wikiPageWikiLink Congruence_(geometry).
- Erlangen_program wikiPageWikiLink Conic_section.
- Erlangen_program wikiPageWikiLink Cross-ratio.
- Erlangen_program wikiPageWikiLink De_Sitter_space.
- Erlangen_program wikiPageWikiLink Diagonal_matrix.
- Erlangen_program wikiPageWikiLink Dimension.
- Erlangen_program wikiPageWikiLink Ehresmann.
- Erlangen_program wikiPageWikiLink Elliptic_geometry.
- Erlangen_program wikiPageWikiLink Euclid.
- Erlangen_program wikiPageWikiLink Euclidean_geometry.
- Erlangen_program wikiPageWikiLink Euclidean_group.
- Erlangen_program wikiPageWikiLink Euclidean_plane_geometry.
- Erlangen_program wikiPageWikiLink Euclidean_space.
- Erlangen_program wikiPageWikiLink Felix_Klein.
- Erlangen_program wikiPageWikiLink Formal_system.
- Erlangen_program wikiPageWikiLink Galois_theory.
- Erlangen_program wikiPageWikiLink General_linear_group.
- Erlangen_program wikiPageWikiLink Geometrical_perspective.
- Erlangen_program wikiPageWikiLink Geometry.
- Erlangen_program wikiPageWikiLink Group_(mathematics).
- Erlangen_program wikiPageWikiLink Group_theory.
- Erlangen_program wikiPageWikiLink Groupoid.
- Erlangen_program wikiPageWikiLink Groupoids.
- Erlangen_program wikiPageWikiLink H.S.M._Coxeter.
- Erlangen_program wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Erlangen_program wikiPageWikiLink Heinrich_Guggenheimer.
- Erlangen_program wikiPageWikiLink Higher_dimensions.
- Erlangen_program wikiPageWikiLink Historia_Mathematica.
- Erlangen_program wikiPageWikiLink Homeomorphism.
- Erlangen_program wikiPageWikiLink Homogeneous_space.
- Erlangen_program wikiPageWikiLink Homography.
- Erlangen_program wikiPageWikiLink Hyperbolic_geometry.
- Erlangen_program wikiPageWikiLink Hyperbolic_motion.
- Erlangen_program wikiPageWikiLink Hyperplane_at_infinity.
- Erlangen_program wikiPageWikiLink Incidence_structure.
- Erlangen_program wikiPageWikiLink Invariant_(mathematics).
- Erlangen_program wikiPageWikiLink Inversive_geometry.
- Erlangen_program wikiPageWikiLink Isomorphic.
- Erlangen_program wikiPageWikiLink Isomorphism.
- Erlangen_program wikiPageWikiLink Jean-Victor_Poncelet.
- Erlangen_program wikiPageWikiLink Jean_Piaget.
- Erlangen_program wikiPageWikiLink John_Baez.
- Erlangen_program wikiPageWikiLink John_C._Baez.
- Erlangen_program wikiPageWikiLink Klein_geometry.
- Erlangen_program wikiPageWikiLink Lie_group.
- Erlangen_program wikiPageWikiLink Logical_system.
- Erlangen_program wikiPageWikiLink Lorentz_group.
- Erlangen_program wikiPageWikiLink Mathematical_structure.
- Erlangen_program wikiPageWikiLink Motion_(geometry).
- Erlangen_program wikiPageWikiLink N-sphere.
- Erlangen_program wikiPageWikiLink Nicolas_Bourbaki.
- Erlangen_program wikiPageWikiLink Non-Euclidean_geometry.
- Erlangen_program wikiPageWikiLink NonEuclidean_geometry.
- Erlangen_program wikiPageWikiLink Orientability.
- Erlangen_program wikiPageWikiLink Oriented.
- Erlangen_program wikiPageWikiLink Orthochronous_Lorentz_group.
- Erlangen_program wikiPageWikiLink Orthogonal_group.
- Erlangen_program wikiPageWikiLink Parallel_(geometry).
- Erlangen_program wikiPageWikiLink Parallel_postulate.
- Erlangen_program wikiPageWikiLink Perspective_(graphical).
- Erlangen_program wikiPageWikiLink Physics.
- Erlangen_program wikiPageWikiLink Poincaré_half-plane_model.
- Erlangen_program wikiPageWikiLink Projective_geometry.
- Erlangen_program wikiPageWikiLink Projective_space.
- Erlangen_program wikiPageWikiLink Projective_transformation.
- Erlangen_program wikiPageWikiLink Radius_of_curvature_(mathematics).