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- Sylvester–Gallai_theorem abstract "The Sylvester–Gallai theorem asserts that given a finite number of points in the Euclidean plane, either all the points are collinear; or there is a line which contains exactly two of the points.This claim was posed as a problem by J. J. Sylvester (1893). Kelly (1986) suggests that Sylvester may have been motivated by a related phenomenon in algebraic geometry, in which the inflection points of a cubic curve in the complex projective plane form a configuration of nine points and twelve lines in which each line determined by two of the points contains a third point. The Sylvester–Gallai theorem implies that it is impossible for all nine of these points to have real coordinates. Woodall (1893) claimed to have a short proof, but it was already noted to be incomplete at the time of publication. Eberhard Melchior (1941) proved the projective dual of this theorem, (actually, of a slightly stronger result). Unaware of Melchior's proof, Paul Erdős (1943) again stated the conjecture, which was proved first by Tibor Gallai, and soon afterwards by other authors.A line that contains exactly two of a set of points is known as an ordinary line. There is an algorithm that finds an ordinary line in a set of n points in time proportional to n log n in the worst case.".
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- Sylvester–Gallai_theorem wikiPageWikiLinkText "2-point lines".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "Melchior's inequality".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "Sylvester's Problem".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "Sylvester's line problem".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "Sylvester–Gallai theorem".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "Sylvester–Gallai theorem#Melchior's inequality".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "the number of 2-point lines".
- Sylvester–Gallai_theorem wikiPageWikiLinkText "two-point lines".
- Sylvester–Gallai_theorem author1Link "Nicolaas Govert de Bruijn".
- Sylvester–Gallai_theorem author2Link "Paul Erdős".
- Sylvester–Gallai_theorem authorlink "Eberhard Melchior".
- Sylvester–Gallai_theorem authorlink "Gabriel Andrew Dirac".
- Sylvester–Gallai_theorem authorlink "Harold Scott MacDonald Coxeter".
- Sylvester–Gallai_theorem authorlink "James Joseph Sylvester".
- Sylvester–Gallai_theorem authorlink "Paul Erdős".
- Sylvester–Gallai_theorem authorlink "Theodore Motzkin".
- Sylvester–Gallai_theorem first "Eberhard".
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