Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-26
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
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A finite projective plane
Definition
A finite projective plane is a finite set of points together with a finite collection of subsets of , called lines, such that:
- every line contains at least three points;
- any two distinct points lie on exactly one line;
- any two distinct lines meet in exactly one point;
- there exist four points no three of which lie on one line.
Used by
- A projective plane of order n is a symmetric 2-(n²+n+1,n+1,1) design Corollary
- The order of a finite projective plane Definition
- The seven translates of {0,1,3} form the Fano plane Example
- Every line in a finite projective plane has the same number of points Lemma
- A finite projective plane of order n has n²+n+1 points and the same number of lines Theorem
- For every prime power q, the space PG(2,q) is a projective plane of order q Theorem
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Noam D. Elkies, Math 155 notes: Feb. 3 (standard reference, not scraped)