imaginary geometry en · NOUN
Etymology
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.
Meanings
-
(uncountable) 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.
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 188:1879, 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.
Relateds
hyperbolic geometry · pangeometry · elliptic geometry
Synonyms
geometry with no parallel postulate
Translations (1)
ru мни́мая геометрия (geometry with no parallel postulate — see also absolute geometry)