imaginary geometry
English
[edit]Etymology
[edit]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.
Noun
[edit]imaginary geometry (uncountable)
- (geometry) 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[Clifford] 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.
- 2011, Seth Braver, Lobachevski Illuminated, Mathematical Association of America, page 188:
- Claim 7. The Euclidean law of cosines holds for any infinitesimal triangle in imaginary geometry.
- 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,
Synonyms
[edit]- (geometry with no parallel postulate): absolute geometry, neutral geometry
Translations
[edit]geometry with no parallel postulate — see also absolute geometry
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See also
[edit]References
[edit]- 2012, Norbert A'Campo, Athanase Papadopoulos, Notes on non-Euclidean geometry, Athanase Papadopoulos (editor), Strasbourg Master Class on Geometry, page 4,
- Lobachevsky used the words imaginary geometry for neutral geometry, and pangeometry for hyperbolic geometry, see the comments on the use of these words and others in [59], p. 230-233.
- Lobachevsky, Pangeometry, English translation, notes and commentary by A. Papadopoulos, Heritage of European Mathematics, Vol. 4, European Mathematics Publishing House, 322 pages, 2010.
