Pseudosphere

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Rotation surface of a tractrix around its asymptote

In differential geometry , the term pseudosphere is used for various surfaces that have a constant negative Gaussian curvature :

Theoretical pseudosphere

In the abstract interpretation, a pseudosphere with radius is a surface with constant Gaussian curvature (precisely a complete , simply connected surface of this curvature), in analogy to a sphere with radius , which is a surface with Gaussian curvature .

The term was introduced in 1868 by Eugenio Beltrami in his work Models of Hyperbolic Geometry .

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