In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix...

of some important conjectures in the Langlands program. Jacquet–Langlands correspondence Erlangen program "Math Quartet Joins Forces on Unified Theory"...

transformation geometry soon appreciates the significance of Felix Klein's Erlangen program, an outgrowth of certain models of hyperbolic geometry. The combination...

Erlangen (German pronunciation: [ˈɛʁlaŋən] ; Mainfränkisch: Erlang, Bavarian: Erlanga) is a Middle Franconian city in Bavaria, Germany. It is the seat...

and the associations between geometry and group theory. His 1872 Erlangen program classified geometries by their basic symmetry groups and was an influential...

1) or Galilean and Carrollian spaces. From the point of view of the Erlangen program, one may understand that "all points are the same", in the geometry...

via invariant theory and the Erlangen program, has an impact in number theory via automorphic forms and the Langlands program. There are many approaches...

approaches from Riemannian geometry of studying invariances, and of the Erlangen program of characterizing geometries according to their group symmetries. The...

Klein coined the term non-Euclidean geometry in 1871, and through the Erlangen program put Euclidean and non-Euclidean geometries on the same footing. Implicitly...

geometries may be created by discarding or modifying them. Following the Erlangen program of Klein, the nature of any given geometry can be seen as the connection...

Silva, anticipated Tarski in applying the Erlangen Program to logic.[citation needed] The Erlangen program classified the various types of geometry (Euclidean...

(1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Graduate Texts in Mathematics. Vol. 166. New York: Springer-Verlag...

is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous space X together with a transitive...

(1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. New York: Springer. ISBN 0-387-94732-9. Snapper, Ernst; Troyer, Robert...

Euclidean geometry. However the converse is not true. Affine geometry Erlangen program Foundations of geometry Incidence geometry Non-Euclidean geometry Faber...

of Erlangen-Nuremberg (German: Friedrich-Alexander-Universität Erlangen-Nürnberg, FAU) is a public research university in the cities of Erlangen and...

homeomorphic or not." The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation...

Such an approach to geometry was cultivated by Felix Klein in his Erlangen program. The idea of reducing geometry to its characteristic group was developed...

quantum mechanics (see Wigner's classification). In accordance with the Erlangen program, the geometry of Minkowski space is defined by the Poincaré group:...

break; } // computed invariant: ICount % 3 == 1 || ICount % 3 == 2 } Erlangen program Graph invariant Invariant differential operator Invariant estimator...

(1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. New York: Springer. ISBN 0-387-94732-9. page 37 Lawson, H. Blaine;...

(1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. New York: Springer. ISBN 0-387-94732-9. Warner, Frank W. (1983). Foundations...

geometry, affine geometry and finite geometry. Finally Felix Klein's "Erlangen program" identified the underlying theme of all of these geometries, defining...

(1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Springer-Verlag, New York. ISBN 0-387-94732-9.. Spivak, Michael (1999)...

cradle of some of the most interesting studies on such issues." The Erlangen program of Felix Klein appealed early on to Segre, and he became a promulgator...

Euclidean spaces given in this article, is essentially issued from his Erlangen program, with the emphasis given on the groups of translations and isometries...

projective geometry and, later, non-Euclidean geometry. Felix Klein's Erlangen program proclaimed group theory to be the organizing principle of geometry...

general concepts of cyclic groups and abelian groups. Klein's 1872 Erlangen program studied geometry and led to symmetry groups such as the Euclidean group...

historical and recent, include Felix Klein's Erlangen program, Hilbert's problems, Langlands program, and the Millennium Prize Problems. In the Mathematics...

already has good intuition. As a prime example of generality, the Erlangen program involved an expansion of geometry to accommodate non-Euclidean geometries...