Pseudosphere

In geometry, a pseudosphere is a surface with constant negative Gaussian curvature.

A pseudosphere of radius $R$ is a surface in $\mathbb {R} ^{3}$ having curvature −1/R² at each point. Its name comes from the analogy with the sphere of radius $R$ , which is a surface of curvature 1/R². The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.^[1]

^ Beltrami, Eugenio (1868). "Saggio sulla interpretazione della geometria non euclidea" [Treatise on the interpretation of non-Euclidean geometry]. Gior. Mat. (in Italian). 6: 248–312.
(Also Beltrami, Eugenio (July 2010). Opere Matematiche [Mathematical Works] (in Italian). Vol. 1. Scholarly Publishing Office, University of Michigan Library. pp. 374–405. ISBN 978-1-4181-8434-6.;
Beltrami, Eugenio (1869). "Essai d'interprétation de la géométrie noneuclidéenne" [Treatise on the interpretation of non-Euclidean geometry]. Annales de l'École Normale Supérieure (in French). 6: 251–288. doi:10.24033/asens.60. Archived from the original on 2016-02-02. Retrieved 2010-07-24.)

[1] Beltrami, Eugenio (1868). "Saggio sulla interpretazione della geometria non euclidea" [Treatise on the interpretation of non-Euclidean geometry]. Gior. Mat. (in Italian). 6: 248–312.
(Also Beltrami, Eugenio (July 2010). Opere Matematiche [Mathematical Works] (in Italian). Vol. 1. Scholarly Publishing Office, University of Michigan Library. pp. 374–405. ISBN 978-1-4181-8434-6.;
Beltrami, Eugenio (1869). "Essai d'interprétation de la géométrie noneuclidéenne" [Treatise on the interpretation of non-Euclidean geometry]. Annales de l'École Normale Supérieure (in French). 6: 251–288. doi:10.24033/asens.60. Archived from the original on 2016-02-02. Retrieved 2010-07-24.)

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