absolute geometry
English
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Etymology
[edit]From 1832; introduced by Hungarian mathematician János Bolyai (1802—1860).
Noun
[edit]absolute geometry (plural absolute geometries)
- (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 [Princeton University Press], 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.
- 1993 [Princeton University Press], Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85,
- (geometry) Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.
- 1970, J. F. Rigby, Axioms for Absolute Geometry, III, Canadian Journal of Mathematics, Vol. XXII, No. 1, Canadian Mathematical Congress, University of Toronto Press, page 185,
- A discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper.
- 1970, J. F. Rigby, Axioms for Absolute Geometry, III, Canadian Journal of Mathematics, Vol. XXII, No. 1, Canadian Mathematical Congress, University of Toronto Press, page 185,
Synonyms
[edit]- (Euclidean geometry without the parallel postulate): neutral geometry
Translations
[edit]Euclidean geometry without the parallel postulate
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See also
[edit]Further reading
[edit]
Foundations of geometry on Wikipedia.Wikipedia - Euclidean geometry on Wikipedia.Wikipedia
- Non-Euclidean geometry on Wikipedia.Wikipedia
- Hyperbolic geometry on Wikipedia.Wikipedia
- Hilbert's axioms on Wikipedia.Wikipedia
- Parallel postulate on Wikipedia.Wikipedia
