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- Happy_ending_problem abstract "The "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement:Theorem: any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.This was one of the original results that led to the development of Ramsey theory.The happy ending theorem can be proven by a simple case analysis: if four or more points are vertices of the convex hull, any four such points can be chosen. If on the other hand, the point set has the form of a triangle with two points inside it, the two inner points and one of the triangle sides can be chosen. See Peterson (2000) for an illustrated explanation of this proof, and Morris & Soltan (2000) for a more detailed survey of the problem.The Erdős–Szekeres conjecture states precisely a more general relationship between the number of points in a general-position point set and its largest convex polygon. It remains unproven, but less precise bounds are known.".
- Happy_ending_problem thumbnail Happy-End-problem.svg?width=300.
- Happy_ending_problem wikiPageExternalLink h.ps.
- Happy_ending_problem wikiPageExternalLink 30toth.pdf.
- Happy_ending_problem wikiPageExternalLink mathtrek_10_3_00.html.
- Happy_ending_problem wikiPageExternalLink item?id=CM_1935__2__463_0.
- Happy_ending_problem wikiPageExternalLink HappyEndingProblem.html.
- Happy_ending_problem wikiPageExternalLink RamseyTheoreticProofOfTheErdHosSzekeresTheorem.html.
- Happy_ending_problem wikiPageExternalLink home.html.
- Happy_ending_problem wikiPageExternalLink 2409.html.
- Happy_ending_problem wikiPageID "2576185".
- Happy_ending_problem wikiPageLength "13711".
- Happy_ending_problem wikiPageOutDegree "34".
- Happy_ending_problem wikiPageRevisionID "655156768".
- Happy_ending_problem wikiPageWikiLink ANZIAM_Journal.
- Happy_ending_problem wikiPageWikiLink American_Mathematical_Monthly.
- Happy_ending_problem wikiPageWikiLink Australian_Mathematical_Society.
- Happy_ending_problem wikiPageWikiLink Canadian_Mathematical_Bulletin.
- Happy_ending_problem wikiPageWikiLink Category:Discrete_geometry.
- Happy_ending_problem wikiPageWikiLink Category:Euclidean_plane_geometry.
- Happy_ending_problem wikiPageWikiLink Category:Mathematical_problems.
- Happy_ending_problem wikiPageWikiLink Category:Ramsey_theory.
- Happy_ending_problem wikiPageWikiLink Complete_graph.
- Happy_ending_problem wikiPageWikiLink Compositio_Mathematica.
- Happy_ending_problem wikiPageWikiLink Convex_hull.
- Happy_ending_problem wikiPageWikiLink Convex_polygon.
- Happy_ending_problem wikiPageWikiLink Convex_polytope.
- Happy_ending_problem wikiPageWikiLink Convex_position.
- Happy_ending_problem wikiPageWikiLink Crossing_number_(graph_theory).
- Happy_ending_problem wikiPageWikiLink Cyclic_polytope.
- Happy_ending_problem wikiPageWikiLink Discrete_and_Computational_Geometry.
- Happy_ending_problem wikiPageWikiLink Erdős–Szekeres_theorem.
- Happy_ending_problem wikiPageWikiLink Esther_Szekeres.
- Happy_ending_problem wikiPageWikiLink Euclidean_space.
- Happy_ending_problem wikiPageWikiLink General_position.
- Happy_ending_problem wikiPageWikiLink George_Szekeres.
- Happy_ending_problem wikiPageWikiLink Graph_drawing.
- Happy_ending_problem wikiPageWikiLink Heptagon.
- Happy_ending_problem wikiPageWikiLink Hexagon.
- Happy_ending_problem wikiPageWikiLink Integer.
- Happy_ending_problem wikiPageWikiLink Neighborly_polytope.
- Happy_ending_problem wikiPageWikiLink Paul_Erdős.
- Happy_ending_problem wikiPageWikiLink Pentagon.
- Happy_ending_problem wikiPageWikiLink PlanetMath.
- Happy_ending_problem wikiPageWikiLink Quadrilateral.
- Happy_ending_problem wikiPageWikiLink Ramsey_theory.
- Happy_ending_problem wikiPageWikiLink Springer-Verlag.
- Happy_ending_problem wikiPageWikiLink Springer_Science+Business_Media.
- Happy_ending_problem wikiPageWikiLink File:8-points-no-pentagon.svg.
- Happy_ending_problem wikiPageWikiLink File:Happy-End-problem.svg.
- Happy_ending_problem wikiPageWikiLinkText "Happy ending problem".
- Happy_ending_problem wikiPageWikiLinkText "happy ending problem".
- Happy_ending_problem hasPhotoCollection Happy_ending_problem.
- Happy_ending_problem title "Happy End Problem".
- Happy_ending_problem urlname "HappyEndProblem".
- Happy_ending_problem wikiPageUsesTemplate Template:Citation.
- Happy_ending_problem wikiPageUsesTemplate Template:For.
- Happy_ending_problem wikiPageUsesTemplate Template:Harvtxt.
- Happy_ending_problem wikiPageUsesTemplate Template:Mathworld.
- Happy_ending_problem wikiPageUsesTemplate Template:Refbegin.
- Happy_ending_problem wikiPageUsesTemplate Template:Refend.
- Happy_ending_problem wikiPageUsesTemplate Template:Reflist.
- Happy_ending_problem subject Category:Discrete_geometry.
- Happy_ending_problem subject Category:Euclidean_plane_geometry.
- Happy_ending_problem subject Category:Mathematical_problems.
- Happy_ending_problem subject Category:Ramsey_theory.
- Happy_ending_problem hypernym Statement.
- Happy_ending_problem type Redirect.
- Happy_ending_problem comment "The "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement:Theorem: any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.This was one of the original results that led to the development of Ramsey theory.The happy ending theorem can be proven by a simple case analysis: if four or more points are vertices of the convex hull, any four such points can be chosen. ".
- Happy_ending_problem label "Happy ending problem".
- Happy_ending_problem sameAs مسألة_نهاية_سعيدة.
- Happy_ending_problem sameAs Problema_del_final_feliç.
- Happy_ending_problem sameAs Problema_del_final_feliz.
- Happy_ending_problem sameAs مسئله_پایان_خوش.
- Happy_ending_problem sameAs Erdősin-Szekeresin_konjektuuri.
- Happy_ending_problem sameAs Happy_Ending_problem.
- Happy_ending_problem sameAs Happy_End-probléma.
- Happy_ending_problem sameAs O_Problema_do_Final_Feliz.
- Happy_ending_problem sameAs m.07p47h.
- Happy_ending_problem sameAs Задача_со_счастливым_концом.
- Happy_ending_problem sameAs ปัญหาแฮปปี้เอ็นดิ้ง.
- Happy_ending_problem sameAs Q1033772.
- Happy_ending_problem sameAs Q1033772.
- Happy_ending_problem sameAs 幸福結局問題.
- Happy_ending_problem wasDerivedFrom Happy_ending_problem?oldid=655156768.
- Happy_ending_problem depiction Happy-End-problem.svg.
- Happy_ending_problem isPrimaryTopicOf Happy_ending_problem.