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- Intersection_theorem abstract "In projective geometry, an intersection theorem or incidence theorem is an incidence structure consisting of points, lines, and possibly higher-dimensional objects and their incidences, together with a pair of nonincident objects A and B (for instance, a point and a line). The "theorem" states that, whenever a set of objects satisfies the incidences (i.e. can be matched up with the objects of the incidence structure in a way that preserves incidence), then objects determined by A and B must also be incident. An intersection theorem is not necessarily true in all projective geometries; it is rather a property which some geometries satisfy but not others.For example, Desargues' theorem can be stated using the following incidence structure:Points: Lines: Incidences (in addition to obvious ones such as The implication is then —that point R is incident with line PQ.".
- Intersection_theorem wikiPageID "5626232".
- Intersection_theorem wikiPageRevisionID "576900618".
- Intersection_theorem hasPhotoCollection Intersection_theorem.
- Intersection_theorem subject Category:Incidence_geometry.
- Intersection_theorem subject Category:Theorems_in_projective_geometry.
- Intersection_theorem type Abstraction100002137.
- Intersection_theorem type Communication100033020.
- Intersection_theorem type Message106598915.
- Intersection_theorem type Proposition106750804.
- Intersection_theorem type Statement106722453.
- Intersection_theorem type Theorem106752293.
- Intersection_theorem type TheoremsInGeometry.
- Intersection_theorem type TheoremsInProjectiveGeometry.
- Intersection_theorem comment "In projective geometry, an intersection theorem or incidence theorem is an incidence structure consisting of points, lines, and possibly higher-dimensional objects and their incidences, together with a pair of nonincident objects A and B (for instance, a point and a line). The "theorem" states that, whenever a set of objects satisfies the incidences (i.e.".
- Intersection_theorem label "Intersection theorem".
- Intersection_theorem sameAs m.0dx0cd.
- Intersection_theorem sameAs Q17101806.
- Intersection_theorem sameAs Q17101806.
- Intersection_theorem sameAs Intersection_theorem.
- Intersection_theorem wasDerivedFrom Intersection_theorem?oldid=576900618.
- Intersection_theorem isPrimaryTopicOf Intersection_theorem.