imaginary geometry
nounEtymology Calque of Russian мни́мая геометрия (mnímaja geometrija), coined by mathematician Nicolai Lobachevsky, probably influenced by мни́мое чи́сло (mnímoje číslo, “imaginary number”), although his precise reasoning is unknown.
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Geometry, Mathematics, Sciences Absolute geometry, an axiomatised geometry in which the parallel postulate is absent and not replaced by an alternative, and of which Euclidean geometry and some non-Euclidean geometries are subtypes.
- 1879, Frederick Pollock, Introduction, Part 1: Biographical, Leslie Stephen, Frederick Pollock (editors), William Kingdon Clifford, Lectures and Essays, Volume 1, Cambridge University Press, page 14, He liked talking about imaginary geometry, as a matter of pure amusement, to anyone interested in it. But at the same time he attached a serious import to it.
- Claim 7. The Euclidean law of cosines holds for any infinitesimal triangle #92;triangleABC in imaginary geometry.2011, Seth Braver, Lobachevski Illuminated, Mathematical Association of America, page 188:
- Synonyms
- geometry with no parallel postulate
- Related terms
- elliptic geometry, hyperbolic geometry, pangeometry