The De Bruijn-Erdos Theorem, published by Nicolaas Govert de Bruijn and Paul Erdos in 1948, gives a lower bound in incidence geometry on the number of lines determined by a set of n points in a projective plane, when those points do not all lie on a single line. By the duality of projective planes, the same bound also applies to the number of intersection points determined by a configuration of lines.
Facts
StatementFor a configuration of n points in a projective plane, not all on one line, the number of lines t determined by those points satisfies t is greater than or equal to n. 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
Source De Bruijn-Erdos theorem (incidence geometry) (Wikipedia)
Proved By
Source De Bruijn-Erdos theorem (incidence geometry) (Wikipedia)
Sources
1. De Bruijn-Erdos theorem (incidence geometry) (Wikipedia)
Statement of the theorem section
Let P be a configuration of n points in a projective plane, not all on a line. Let t be the number of lines determined by P. Then, t ≥ n
Lead section
originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948
- In Branch: Geometry, Lead sentence
Proved By: Nicolaas Govert de Bruijn, Lead paragraph
In incidence geometry, the De Bruijn-Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on the number
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