英和和英

名詞

imaginary geometry (uncountable)

1. (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 ${\displaystyle \triangle ABC}$ in imaginary geometry.

同意語

• (幾何学 with no parallel postulate): absolute geometry, neutral geometry

参考

• elliptic geometry
• hyperbolic geometry
• pangeometry

参照

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.

Further reading

• Absolute geometry on Wikipedia.
• Lobachevskii geometry on Encyclopedia of Mathematics
• Absolute Geometry on Wolfram MathWorld