|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:can_be_constructed_from
|
Finite fields
|
|
gptkbp:Desarguesian_plane
|
Constructed from finite fields
|
|
gptkbp:each_line_contains
|
n+1 points
|
|
gptkbp:each_point_lies_on
|
n+1 lines
|
|
gptkbp:every_two_lines_meet_at
|
Exactly one point
|
|
gptkbp:every_two_points_determine
|
Exactly one line
|
|
gptkbp:example
|
gptkb:Fano_plane
|
|
gptkbp:Fano_plane_order
|
2
|
|
gptkbp:field
|
gptkb:Mathematics
|
|
gptkbp:hasAxiom
|
Any two lines meet at a unique point
Any two points lie on a unique line
There exist four points, no three collinear
|
|
gptkbp:hasProperty
|
Finite number of lines
Finite number of points
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Finite projective plane
|
|
gptkbp:line
|
n^2 + n + 1
|
|
gptkbp:non-Desarguesian_examples
|
Exist for some orders
|
|
gptkbp:number_of_points
|
n^2 + n + 1
|
|
gptkbp:order
|
n (if each line contains n+1 points)
|
|
gptkbp:order_10
|
Existence unknown
|
|
gptkbp:order_6
|
Does not exist
|
|
gptkbp:relatedTo
|
gptkb:Steiner_system
Block design
Incidence geometry
|
|
gptkbp:subclassOf
|
gptkb:Projective_plane
|
|
gptkbp:used_in
|
Combinatorics
Coding theory
Design theory
Finite geometry
|
|
gptkbp:bfsParent
|
gptkb:Projective_plane
|
|
gptkbp:bfsLayer
|
7
|