Absolute geometry
Geometry without the parallel postulate / From Wikipedia, the free encyclopedia
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Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates.[1] The term was introduced by János Bolyai in 1832.[2] It is sometimes referred to as neutral geometry,[3] as it is neutral with respect to the parallel postulate. The first four of Euclid's postulates are now considered insufficient as a basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead.[4]