Imaginary geometry

English

Etymology

Template:Calque, coined by mathematician Template:W, probably influenced by Template:M, although his precise reasoning is unknown.

Noun

1. Template:Lb 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), Template:W, Lectures and Essays, Volume 1, Template:W, 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.

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Synonyms

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Translations

• Russian: Template:T

See also

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References

1. 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.

2. Lobachevsky, Pangeometry, English translation, notes and commentary by A. Papadopoulos, Heritage of European Mathematics, Vol. 4, European Mathematics Publishing House, 322 pages, 2010.

Further reading

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• Lobachevskii geometry on Template:W
• Absolute Geometry on Template:W