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gptkbp:instanceOf
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gptkb:geometry
gptkb:mathematical_concept
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gptkbp:application
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gptkb:Computer_graphics
gptkb:Algebraic_geometry
Perspective drawing
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gptkbp:chromaticNumber
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6 (real projective plane)
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gptkbp:coordinates
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gptkb:Homogeneous_coordinates
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gptkbp:defines
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A geometric structure that extends the concept of a plane, where any two lines intersect in exactly one point.
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gptkbp:dimensions
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2
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gptkbp:Euler_characteristic
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1
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gptkbp:example
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gptkb:Complex_projective_plane
gptkb:Finite_projective_plane
gptkb:Real_projective_plane
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gptkbp:field
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gptkb:Projective_geometry
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gptkbp:finite_example
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gptkb:Fano_plane
gptkb:Projective_plane_of_order_2
gptkb:Projective_plane_of_order_3
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gptkbp:generalizes
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gptkb:Affine_plane
Euclidean plane
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gptkbp:hasAxiom
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Any two distinct lines meet at a unique point
Any two distinct points lie on a unique line
There exist four points, no three of which are collinear
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https://www.w3.org/2000/01/rdf-schema#label
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Projective plane
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gptkbp:minimum_lines
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7
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gptkbp:minimum_points
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7
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gptkbp:namedAfter
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gptkb:Projective_geometry
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gptkbp:property
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gptkb:Homogeneous_coordinates
Closed surface (real projective plane)
Compact (real projective plane)
Duality between points and lines
Every pair of lines meets
Every pair of points joined by a line
No parallel lines
Non-orientable (real projective plane)
Self-dual structure
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gptkbp:relatedConcept
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gptkb:Desargues'_theorem
gptkb:Fano_plane
gptkb:Pappus's_theorem
gptkb:Affine_plane
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gptkbp:studiedBy
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gptkb:Blaise_Pascal
gptkb:David_Hilbert
gptkb:Felix_Klein
gptkb:Jean-Victor_Poncelet
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gptkbp:symbol
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gptkb:RP^2
gptkb:CP^2
gptkb:PG(2,_K)
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gptkbp:topology
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Non-orientable surface
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gptkbp:bfsParent
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gptkb:Bézout's_theorem
gptkb:Projective_variety
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gptkbp:bfsLayer
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6
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