Absolute Geometry

Absolute geometry is a geometry based on an axiom system for Euclidean geometry that does not assume the parallel postulate or any of its alternatives. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate.

Read more about Absolute GeometryRelation To Other Geometries, Incompleteness

Other articles related to "geometry, absolute geometry":

Axiomatic Basis of Non-Euclidean Geometry
... Euclidean geometry can be axiomatically described in several ways ... Other systems, using different sets of undefined terms obtain the same geometry by different paths ... postulate, in whatever form it takes, and leaving all the other axioms intact, produces absolute geometry ...
Absolute Geometry - Incompleteness
... Absolute geometry is an incomplete axiomatic system, in the sense that one can add extra independent axioms without making the axiom system inconsistent ... One can extend absolute geometry by adding different axioms about parallel lines and get incompatible but consistent axiom systems, giving rise to Euclidean or hyperbolic geometry ... Thus every theorem of absolute geometry is a theorem of hyperbolic geometry and Euclidean geometry ...

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