Changes

==Etymology==

==Etymology==

Late [[Latin]] configuration-, configuratio similar formation, from Latin configurare to form from or after, from com- + figurare to form, from figura figure

Late [[Latin]] configuration-, configuratio similar formation, from Latin configurare to form from or after, from com- + figurare to form, from figura figure

*Date: [http://en.wikipedia.org/wiki/16th_Century 1559]

*Date: [https://en.wikipedia.org/wiki/16th_Century 1559]

==Definitions==

==Definitions==

*1 a : [[relative]] arrangement of parts or elements: as (1) : shape (2) : contour of land <configuration of the mountains> (3) : functional arrangement <a small business computer [[system]] in its simplest configuration>  

*1 a : [[relative]] arrangement of parts or elements: as (1) : shape (2) : contour of land <configuration of the mountains> (3) : functional arrangement <a small business computer [[system]] in its simplest configuration>  

*2 : gestalt <[[personality]] configuration>

*2 : gestalt <[[personality]] configuration>

==Description (Geometry)==

==Description (Geometry)==

In [[mathematics]], specifically [http://en.wikipedia.org/wiki/Projective_geometry projective geometry], a configuration in the [[plane]] consists of a [[finite]] set of points, and a finite [http://en.wikipedia.org/wiki/Arrangement_of_lines 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.

In [[mathematics]], specifically [https://en.wikipedia.org/wiki/Projective_geometry projective geometry], a configuration in the [[plane]] consists of a [[finite]] set of points, and a finite [https://en.wikipedia.org/wiki/Arrangement_of_lines 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.

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 [http://en.wikipedia.org/wiki/Desargues%27_theorem Desargues' theorem]. [http://en.wikipedia.org/wiki/Ernst_Steinitz Ernst Steinitz] wrote his dissertation on the subject in 1894, and they were popularized by Hilbert and Cohn-Vossen's 1932 [[book]] ''Anschaulische Geometrie'' (reprinted in [[English]] as ''Geometry and the Imagination'').

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 [https://en.wikipedia.org/wiki/Desargues%27_theorem Desargues' theorem]. [https://en.wikipedia.org/wiki/Ernst_Steinitz Ernst Steinitz] wrote his dissertation on the subject in 1894, and they were popularized by Hilbert and Cohn-Vossen's 1932 [[book]] ''Anschaulische Geometrie'' (reprinted in [[English]] as ''Geometry and the Imagination'').

Configurations may be studied either as concrete sets of points and lines in a specific [[geometry]], such as the [http://en.wikipedia.org/wiki/Euclidean_plane Euclidean] or projective planes, or as [[abstract]] incidence [[structures]]. In the latter case they are closely related to regular hypergraphs and regular bipartite graphs.[http://en.wikipedia.org/wiki/Configuration_%28geometry%29]

Configurations may be studied either as concrete sets of points and lines in a specific [[geometry]], such as the [https://en.wikipedia.org/wiki/Euclidean_plane Euclidean] or projective planes, or as [[abstract]] incidence [[structures]]. In the latter case they are closely related to regular hypergraphs and regular bipartite graphs.[https://en.wikipedia.org/wiki/Configuration_%28geometry%29]

==References==

==References==

* Berman, Leah W., "[http://www.combinatorics.org/Volume_13/Abstracts/v13i1r104.html Movable (n4) configurations]", The Electronic Journal of Combinatorics 13 (1): R104, http://www.combinatorics.org/Volume_13/Abstracts/v13i1r104.html . See also Berman's animations of movable configurations.

* Berman, Leah W., "[https://www.combinatorics.org/Volume_13/Abstracts/v13i1r104.html Movable (n4) configurations]", The Electronic Journal of Combinatorics 13 (1): R104, https://www.combinatorics.org/Volume_13/Abstracts/v13i1r104.html . See also Berman's animations of movable configurations.

* Betten, A; Brinkmann, G.; Pisanski, T. (2000), "Counting symmetric configurations", Discrete Applied Mathematics 99 (1–3): 331–338, doi:10.1016/S0166-218X(99)00143-2 .

* Betten, A; Brinkmann, G.; Pisanski, T. (2000), "Counting symmetric configurations", Discrete Applied Mathematics 99 (1–3): 331–338, doi:10.1016/S0166-218X(99)00143-2 .

* Coxeter, H.S.M. (1948), [http://en.wikipedia.org/wiki/Regular_Polytopes_(book) Regular Polytopes], Methuen and Co .

* Coxeter, H.S.M. (1948), [https://en.wikipedia.org/wiki/Regular_Polytopes_(book) Regular Polytopes], Methuen and Co .

* Gropp, Harald (1997), "Configurations and their realization", [http://en.wikipedia.org/wiki/Discrete_Mathematics_(journal) Discrete Mathematics] 174 (1–3): 137–151, doi:10.1016/S0012-365X(96)00327-5 .

* Gropp, Harald (1997), "Configurations and their realization", [https://en.wikipedia.org/wiki/Discrete_Mathematics_(journal) Discrete Mathematics] 174 (1–3): 137–151, doi:10.1016/S0012-365X(96)00327-5 .

* [http://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaum Grünbaum, Branko] (2006), "Configurations of points and lines", in Davis, Chandler; Ellers, Erich W., The Coxeter Legacy: Reflections and Projections, American Mathematical Society, pp. 179–225 .

* [https://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaum Grünbaum, Branko] (2006), "Configurations of points and lines", in Davis, Chandler; Ellers, Erich W., The Coxeter Legacy: Reflections and Projections, American Mathematical Society, pp. 179–225 .

* Grünbaum, Branko (2009), Configurations of Points and Lines, Graduate Studies in Mathematics, 103, American Mathematical Society, ISBN 978-0-8218-4308-6 .

* Grünbaum, Branko (2009), Configurations of Points and Lines, Graduate Studies in Mathematics, 103, American Mathematical Society, ISBN 978-0-8218-4308-6 .

* Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), Chelsea, pp. 94–170, ISBN 0-8284-1087-9 .

* Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), Chelsea, pp. 94–170, ISBN 0-8284-1087-9 .

* Kelly, L. M. (1986), "A resolution of the Sylvester–Gallai problem of J. P. Serre", [http://en.wikipedia.org/wiki/Discrete_and_Computational_Geometry Discrete and Computational Geometry] 1 (1): 101–104, doi:10.1007/BF02187687 .

* Kelly, L. M. (1986), "A resolution of the Sylvester–Gallai problem of J. P. Serre", [https://en.wikipedia.org/wiki/Discrete_and_Computational_Geometry Discrete and Computational Geometry] 1 (1): 101–104, doi:10.1007/BF02187687 .

==External links==

==External links==

* Weisstein, Eric W., "[http://mathworld.wolfram.com/Configuration.html Configuration]" from MathWorld.

* Weisstein, Eric W., "[https://mathworld.wolfram.com/Configuration.html Configuration]" from MathWorld.

[[Category: Mathematics]]

[[Category: Mathematics]]