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

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

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

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

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

formalism of powerful analytical methods. Jacquet–Langlands correspondence Erlangen program "Math Quartet Joins Forces on Unified Theory". Quanta. December 8,...

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...

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

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...

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

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...

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

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

between symmetry and geometry came under intense scrutiny. Felix Klein's Erlangen program proclaimed that, in a very precise sense, symmetry, expressed via the...

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

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

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...

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

(2000). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Springer. p. 194. ISBN 978-0-387-94732-7. Schouten, Jan Arnoldus (1954)...

Lorentz transformations in special relativity. Coordinate transformation Erlangen program Symmetry (geometry) Motion Reflection Rigid transformation Rotation...

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

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

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...

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

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

with Maupertuis's principle in the 18th century. Felix Klein's 1872 Erlangen program attempted to identify invariants under a group of transformations....

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

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

non-Euclidean geometry History of topology History of algebraic geometry Erlangen program Noncommutative geometry Topology Convex hull construction Euclidean...

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