Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Erlangen_program> ?p ?o. }
Showing items 1 to 47 of
47
with 100 items per page.
- Erlangen_program abstract "An influential research program and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen. This Erlangen Program (Erlanger Programm)—Klein was then at Erlangen—proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory.At that time, a family of new non-Euclidean geometries had already emerged, without adequate clarifications of their mutual hierarchy and relationships. Klein's suggestion 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.Ultimately Élie Cartan generalized Klein's homogeneous model spaces to (Cartan) connections on certain principal bundles. Simultaneously, this view generalizes classical 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 wikiPageRevisionID "604069973".
- Erlangen_program hasPhotoCollection Erlangen_program.
- Erlangen_program id "p/e036190".
- Erlangen_program title "Erlangen program".
- Erlangen_program subject Category:Classical_geometry.
- Erlangen_program subject Category:Erlangen.
- Erlangen_program subject Category:Group_theory.
- Erlangen_program subject Category:Homogeneous_spaces.
- Erlangen_program subject Category:Symmetry.
- Erlangen_program type Abstraction100002137.
- Erlangen_program type Attribute100024264.
- Erlangen_program type HomogeneousSpaces.
- Erlangen_program type Space100028651.
- Erlangen_program comment "An influential research program and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen.".
- Erlangen_program label "Erlangen program".
- Erlangen_program label "Erlanger Programm".
- Erlangen_program label "Erlanger Programm".
- Erlangen_program label "Program erlangeński".
- Erlangen_program label "Programa de Erlangen".
- Erlangen_program label "Programa de Erlangen".
- Erlangen_program label "Programma di Erlangen".
- Erlangen_program label "Programme d'Erlangen".
- Erlangen_program label "Эрлангенская программа".
- Erlangen_program label "برنامج إرلنغن".
- Erlangen_program label "エルランゲン・プログラム".
- Erlangen_program label "爱尔兰根纲领".
- Erlangen_program sameAs Erlanger_Programm.
- Erlangen_program sameAs Programa_de_Erlangen.
- Erlangen_program sameAs Programme_d'Erlangen.
- Erlangen_program sameAs Programma_di_Erlangen.
- Erlangen_program sameAs エルランゲン・プログラム.
- Erlangen_program sameAs 에를랑겐_프로그램.
- Erlangen_program sameAs Erlanger_Programm.
- Erlangen_program sameAs Program_erlangeński.
- Erlangen_program sameAs Programa_de_Erlangen.
- Erlangen_program sameAs m.01k8tb.
- Erlangen_program sameAs Q315296.
- Erlangen_program sameAs Q315296.
- Erlangen_program sameAs Erlangen_program.
- Erlangen_program wasDerivedFrom Erlangen_program?oldid=604069973.
- Erlangen_program isPrimaryTopicOf Erlangen_program.