Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
projective plane |
| gptkbp:automorphismGroup |
gptkb:PGL(3,K)
|
| gptkbp:definedIn |
gptkb:field_K
|
| gptkbp:dimensions |
2
|
| gptkbp:example |
Fano plane when K=GF(2)
|
| gptkbp:hasAxiom |
any two lines meet in a unique point
any two points determine a unique line there exist four points, no three collinear |
| gptkbp:hasPoint |
1-dimensional subspaces of K^3
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective geometry PG(2,K)
|
| gptkbp:incidenceRelation |
point lies on line if subspace inclusion holds
|
| gptkbp:line |
(K^3 - {0})/(K^*), if K is finite
|
| gptkbp:linesAre |
2-dimensional subspaces of K^3
|
| gptkbp:notation |
gptkb:PG(2,K)
|
| gptkbp:pointsSystem |
(K^3 - {0})/(K^*), if K is finite
|
| gptkbp:relatedTo |
gptkb:Desargues'_theorem
homogeneous coordinates collineation projective duality projective transformation |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry combinatorics |
| gptkbp:bfsParent |
gptkb:Desarguesian_plane
|
| gptkbp:bfsLayer |
7
|