In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb...

non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein...

opposite each other are identified (considered to be the same). The pseudosphere has the appropriate curvature to model hyperbolic geometry. The simplest...

asymptote: the pseudosphere. Studied by Eugenio Beltrami in 1868, as a surface of constant negative Gaussian curvature, the pseudosphere is a local model...

surfaces of class C2 immersed in R3, but breaks down for C1-surfaces. The pseudosphere has constant negative Gaussian curvature except at its boundary circle...

onto itself. (A similar effect can be seen in the tubular shape of the pseudosphere.) The brown line on the diagram is the worldline of Earth (or more precisely...

plane can be placed onto a pseudosphere and maintain angles and hyperbolic distances, as well as be bent around the pseudosphere and still keep its properties...

relative velocities of "nearby" points (velocities). There exist various pseudospheres in Euclidean space that have a finite area of constant negative Gaussian...

surface with constant negative curvature that can be created by twisting a pseudosphere. It is named after Ulisse Dini and described by the following parametric...

that lacks a boundary with constant, positive Gaussian curvature. The pseudosphere is an example of a surface with constant negative Gaussian curvature...