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.
Facts
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
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
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.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.