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What (who) is kinematic geometry - definition

TWO GEOMETRIES BASED ON AXIOMS CLOSELY RELATED TO THOSE SPECIFYING EUCLIDEAN GEOMETRY

Non-euclidean geometries; NonEuclidean geometry; Non-Euclidean; Noneuclidean geometry; Non-Euclidian geometry; Non-Euclidean geometries; Non-euclidian geometry; Models of non-Euclidean geometry; Non-Euclidena geometry; Non-Euclidean space; Non-Euclidean Geometry; Non euclidian geometry; Models of Non-Euclidean geometry; Non-euclidean Geometry; Non-euclidean geometry; History of non-Euclidean geometry; Kinematic geometry

Models of non-Euclidean geometry

Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A parallel to l, and in elliptic geometric models, parallel lines do not exist.

https://en.wikipedia.org/wiki/Models_of_non-Euclidean_geometry

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.

https://en.wikipedia.org/wiki/Non-Euclidean_geometry

non-Euclidean

¦ adjective denoting systems of geometry that do not obey Euclidean postulates, especially that only one line through a given point can be parallel to a given line.

Wikipedia

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry.

https://en.wikipedia.org/wiki/Non-Euclidean geometry