The Sylvester-Gallai Theorem states that given a finite set of points in the plane that are not all collinear, there always exists a line passing through exactly two of them. First posed as a problem by James Joseph Sylvester and later proved by Tibor Gallai, it is a foundational result in combinatorial geometry.
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StatementThe Sylvester-Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of them. 1 Classification
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Source Sylvester-Gallai Theorem (Wikipedia)
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1. Sylvester-Gallai Theorem (Wikipedia)
Wikimedia FoundationLead paragraph, first sentence
The Sylvester-Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of them.
Lead paragraph, naming sentence
It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944.
Proved By: Tibor Gallai, Lead
Unaware of Melchior's proof, Paul Erdős (1943) again stated the conjecture, which was subsequently proved by Tibor Gallai, and soon afterwards by other authors.
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