absolute geometry

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English

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Etymology

From 1832; introduced by Hungarian mathematician János Bolyai (1802—1860).

Noun

absolute geometry (plural absolute geometries)

  1. (geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.
    • 1993 , Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85,
      Recall that absolute geometry is the set of statements that can be deduced from Euclid's first four postulates. Then existence of parallel lines is certainly a theorem of absolute geometry, while the question being addressed by most of the mathematicians discussed in this section is whether uniqueness of parallels is also a theorem of absolute geometry.
  2. (geometry) Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.

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