Definition of Pseudosphere. Meaning of Pseudosphere. Synonyms of Pseudosphere

Here you will find one or more explanations in English for the word Pseudosphere. Also in the bottom left of the page several parts of wikipedia pages related to the word Pseudosphere and, of course, Pseudosphere synonyms and on the right images related to the word Pseudosphere.

Definition of Pseudosphere

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.

Meaning of Pseudosphere from wikipedia

- 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...
- examples of generalized pseudospheres. There is a correspondence between embedded surfaces of constant curvature -1, known as pseudospheres, and solutions to...
- that lacks a boundary with constant, positive Gaussian curvature. The pseudosphere is an example of a surface with constant negative Gaussian curvature...
- asymptote: the pseudosphere. Studied by Eugenio Beltrami in 1868, as a surface of constant negative Gaussian curvature, the pseudosphere is a local model...
- 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...
- singular due to the Hilbert embedding theorem. In the simplest case, the pseudosphere, also known as the tractroid, corresponds to a static one-soliton, but...
- 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...