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- Q1033772 subject Q6770414.
- Q1033772 subject Q7036101.
- Q1033772 subject Q7132787.
- Q1033772 subject Q7413853.
- Q1033772 abstract "Template:ForThe "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.".
- Q1033772 thumbnail Happy-End-problem.svg?width=300.
- Q1033772 wikiPageExternalLink 30toth.pdf.
- Q1033772 wikiPageExternalLink mathtrek_10_3_00.html.
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- Q1033772 wikiPageWikiLink Q6770414.
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- Q1033772 wikiPageWikiLink Q7413853.
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- Q1033772 comment "Template:ForThe "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. ".
- Q1033772 label "Happy ending problem".
- Q1033772 depiction Happy-End-problem.svg.