What is "pseudosphere"

Pseudosphere \Pseu"do*sphere`\, n. [Pseudo- + sphere.] (Geom.) The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.

n. 1 (context geometry English) A surface generated by rotating a tractrix about its asymptote; a tractricoid 2 (context geometry English) Any of various surfaces with constant negative Gaussian curvature.

In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature. Depending on context, it can refer to either a theoretical surface of constant negative curvature, to a tractricoid, or to a hyperboloid. __TOC__