pseudospheren.

Brit.

/ˈs(j)uːdə(ʊ)sfɪə/, U.S.

/ˈsudoʊˌsfɪ(ə)r/

Origin: Formed within English, by compounding. Etymons: pseudo- comb. form, sphere n.

Etymology: < pseudo- comb. form + sphere n., after pseudospherical adj.The relevant articles by E. Beltrami ( Giornale di matematiche (1868) 6 284–312, Annali di matematica (1869) 2 232–55) only use Italian pseudosferico (adjective), but not the noun pseudosfera.

Mathematics.

The pseudospherical surface that is generated by rotating a tractrix about its asymptote.

ΘΚΠ

the world > relative properties > number > geometry > surface > [noun] > generated by rotation or twisting

pseudosphere1884

Möbius surface1900

Möbius strip1904

Möbius band1932

Klein bottle1941

1884 A. Cayley in Proc. Royal Soc. 37 82 I consider the hyperbolic or Lobatschewskian geometry:..the imaginary spherical surface x² + y² + z² = −1..may be bent (without extension or contraction) into the real surface considered by Beltrami, and which I will call the Pseudosphere.

1909 L. P. Eisenhart Treat. Differential Geom. Curves & Surfaces viii. 274 The surface of revolution of a tractrix about its asymptote is called the pseudosphere, or the pseudospherical surface of the parabolic type.

1965 J. D. North Measure of Universe iv. 60 In 1868 E. Beltrami..showed that Lobachevsky's plane geometry holds in Euclidean space on certain surfaces of constant negative curvature (the pseudospheres) and that these could be conformally represented on a plane.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) viii. 201 The pseudosphere serves as a model for non-Euclidean hyperbolic geometry, just as a sphere does for non-Euclidean elliptic geometry.

This entry has been updated (OED Third Edition, September 2007; most recently modified version published online March 2022).

单词	pseudosphere
释义	pseudospheren. Brit. /ˈs(j)uːdə(ʊ)sfɪə/, U.S. /ˈsudoʊˌsfɪ(ə)r/ Origin: Formed within English, by compounding. Etymons: pseudo- comb. form, sphere n. Etymology: < pseudo- comb. form + sphere n., after pseudospherical adj.The relevant articles by E. Beltrami ( Giornale di matematiche (1868) 6 284–312, Annali di matematica (1869) 2 232–55) only use Italian pseudosferico (adjective), but not the noun pseudosfera. Mathematics. The pseudospherical surface that is generated by rotating a tractrix about its asymptote. ΘΚΠ the world > relative properties > number > geometry > surface > [noun] > generated by rotation or twisting pseudosphere1884 Möbius surface1900 Möbius strip1904 Möbius band1932 Klein bottle1941 1884 A. Cayley in Proc. Royal Soc. 37 82 I consider the hyperbolic or Lobatschewskian geometry:..the imaginary spherical surface x² + y² + z² = −1..may be bent (without extension or contraction) into the real surface considered by Beltrami, and which I will call the Pseudosphere. 1909 L. P. Eisenhart Treat. Differential Geom. Curves & Surfaces viii. 274 The surface of revolution of a tractrix about its asymptote is called the pseudosphere, or the pseudospherical surface of the parabolic type. 1965 J. D. North Measure of Universe iv. 60 In 1868 E. Beltrami..showed that Lobachevsky's plane geometry holds in Euclidean space on certain surfaces of constant negative curvature (the pseudospheres) and that these could be conformally represented on a plane. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) viii. 201 The pseudosphere serves as a model for non-Euclidean hyperbolic geometry, just as a sphere does for non-Euclidean elliptic geometry. This entry has been updated (OED Third Edition, September 2007; most recently modified version published online March 2022). < n.1884
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