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- Configuration_(geometry) abstract "In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.Although certain specific configurations had been studied earlier (for instance by Thomas Kirkman in 1849), the formal study of configurations was first introduced by Theodor Reye in 1876, in the second edition of his book Geometrie der Lage, in the context of a discussion of Desargues' theorem. Ernst Steinitz wrote his dissertation on the subject in 1894, and they were popularized by Hilbert and Cohn-Vossen's 1932 book Anschauliche Geometrie, reprinted in English (Hilbert & Cohn-Vossen 1952).Configurations may be studied either as concrete sets of points and lines in a specific geometry, such as the Euclidean or projective planes (these are said to be realizable in that geometry), or as abstract incidence structures. In the latter case they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions: every two points of the incidence structure can be associated with at most one line, and every two lines can be associated with at most one point. That is, the girth of the corresponding bipartite graph (the Levi graph of the configuration) must be at least six.".
- Configuration_(geometry) thumbnail Complete-quads.svg?width=300.
- Configuration_(geometry) wikiPageExternalLink books?id=bnh2zkuTZr4C.
- Configuration_(geometry) wikiPageExternalLink v13i1r104.html.
- Configuration_(geometry) wikiPageID "7200539".
- Configuration_(geometry) wikiPageRevisionID "604892449".
- Configuration_(geometry) hasPhotoCollection Configuration_(geometry).
- Configuration_(geometry) title "Configuration".
- Configuration_(geometry) urlname "Configuration".
- Configuration_(geometry) subject Category:Configurations.
- Configuration_(geometry) type Abstraction100002137.
- Configuration_(geometry) type Arrangement105726596.
- Configuration_(geometry) type Cognition100023271.
- Configuration_(geometry) type Configuration105731779.
- Configuration_(geometry) type Configurations.
- Configuration_(geometry) type Design105728678.
- Configuration_(geometry) type PsychologicalFeature100023100.
- Configuration_(geometry) type Structure105726345.
- Configuration_(geometry) comment "In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.Although certain specific configurations had been studied earlier (for instance by Thomas Kirkman in 1849), the formal study of configurations was first introduced by Theodor Reye in 1876, in the second edition of his book Geometrie der Lage, in the context of a discussion of Desargues' theorem. ".
- Configuration_(geometry) label "Configuratie (wiskunde)".
- Configuration_(geometry) label "Configuration (geometry)".
- Configuration_(geometry) sameAs Configuratie_(wiskunde).
- Configuration_(geometry) sameAs m.025vy1s.
- Configuration_(geometry) sameAs Q1866689.
- Configuration_(geometry) sameAs Q1866689.
- Configuration_(geometry) sameAs Configuration_(geometry).
- Configuration_(geometry) wasDerivedFrom Configuration_(geometry)?oldid=604892449.
- Configuration_(geometry) depiction Complete-quads.svg.
- Configuration_(geometry) isPrimaryTopicOf Configuration_(geometry).