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- Affine_plane_(incidence_geometry) abstract "In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Each line has at least two points. Given any line and any point not on that line there is a unique line which contains the point and does not meet the given line. (Playfair's axiom) There exist three non-collinear points (points not on a single line).In an affine plane, two lines are called parallel if they are equal or disjoint. Using this definition, Playfair's axiom above can be replaced by: Given a point and a line, there is a unique line which contains the point and is parallel to the line.Parallelism is an equivalence relation on the lines of an affine plane. Since no concepts other than those involving the relationship between points and lines are involved in the axioms, an affine plane is an object of study belonging to incidence geometry. They are non-degenerate linear spaces satisfying Playfair's axiom. The familiar Euclidean plane is an affine plane. There are many finite and infinite affine planes. As well as affine planes over fields (and division rings), there are also many non-Desarguesian planes, not derived from coordinates in a division ring, satisfying these axioms. The Moulton plane is an example of one of these.".
- Affine_plane_(incidence_geometry) thumbnail Hesse_configuration.svg?width=300.
- Affine_plane_(incidence_geometry) wikiPageExternalLink pps.
- Affine_plane_(incidence_geometry) wikiPageID "649724".
- Affine_plane_(incidence_geometry) wikiPageLength "13799".
- Affine_plane_(incidence_geometry) wikiPageOutDegree "40".
- Affine_plane_(incidence_geometry) wikiPageRevisionID "670697878".
- Affine_plane_(incidence_geometry) wikiPageWikiLink Affine_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Affine_space.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Bruck–Ryser–Chowla_theorem.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Category:Geometry.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Category:Incidence_geometry.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Characteristic_(algebra).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Characteristic_(field).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Collineation.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Desarguesian_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Division_ring.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Equivalence_relation.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Euclidean_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Fano_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Field_(mathematics).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Geometry.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Graeco-Latin_square.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Group_action.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Hesse_configuration.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Incidence_geometry.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Incidence_matrix.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Incidence_structure.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Line_at_infinity.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Linear_code.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Linear_space_(geometry).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Moulton_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Mutually_orthogonal_latin_square.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Non-Desarguesian_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Playfairs_axiom.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Point_at_infinity.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Projective_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Projective_space.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Reed-Muller_Code.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Reed–Muller_code.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Transitive_(group_action).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Transitive_property.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Transitive_relation.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Translation_(geometry).
- Affine_plane_(incidence_geometry) wikiPageWikiLink Translation_plane.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Two-dimensional_space.
- Affine_plane_(incidence_geometry) wikiPageWikiLink Vector_space.
- Affine_plane_(incidence_geometry) wikiPageWikiLink File:Hesse_configuration.svg.
- Affine_plane_(incidence_geometry) wikiPageWikiLinkText "affine plane".
- Affine_plane_(incidence_geometry) wikiPageWikiLinkText "affine planes".
- Affine_plane_(incidence_geometry) wikiPageWikiLinkText "affine".
- Affine_plane_(incidence_geometry) wikiPageWikiLinkText "finite affine planes".
- Affine_plane_(incidence_geometry) hasPhotoCollection Affine_plane_(incidence_geometry).
- Affine_plane_(incidence_geometry) wikiPageUsesTemplate Template:Citation.
- Affine_plane_(incidence_geometry) wikiPageUsesTemplate Template:Main.
- Affine_plane_(incidence_geometry) wikiPageUsesTemplate Template:Math.
- Affine_plane_(incidence_geometry) wikiPageUsesTemplate Template:Mergeto.
- Affine_plane_(incidence_geometry) wikiPageUsesTemplate Template:Reflist.
- Affine_plane_(incidence_geometry) subject Category:Geometry.
- Affine_plane_(incidence_geometry) subject Category:Incidence_geometry.
- Affine_plane_(incidence_geometry) hypernym System.
- Affine_plane_(incidence_geometry) comment "In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Each line has at least two points. Given any line and any point not on that line there is a unique line which contains the point and does not meet the given line. (Playfair's axiom) There exist three non-collinear points (points not on a single line).In an affine plane, two lines are called parallel if they are equal or disjoint.".
- Affine_plane_(incidence_geometry) label "Affine plane (incidence geometry)".
- Affine_plane_(incidence_geometry) sameAs Affine_Ebene.
- Affine_plane_(incidence_geometry) sameAs Plan_affine_(structure_dincidence).
- Affine_plane_(incidence_geometry) sameAs m.0gfh4mr.
- Affine_plane_(incidence_geometry) sameAs Q382491.
- Affine_plane_(incidence_geometry) sameAs Q382491.
- Affine_plane_(incidence_geometry) wasDerivedFrom Affine_plane_(incidence_geometry)?oldid=670697878.
- Affine_plane_(incidence_geometry) depiction Hesse_configuration.svg.
- Affine_plane_(incidence_geometry) isPrimaryTopicOf Affine_plane_(incidence_geometry).