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The pseudospherical surface generated by revolving a tractrix about its asymptote.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



the surface of constant negative curvature formed by the rotation of a tractrix about its asymptote (see Figure 1). Its name emphasizes both its similarity to and difference from a sphere, which is an example of a surface with constant positive curvature. The pseudosphere is of particular interest because figures drawn on smooth parts of this surface

obey the laws of Lobachevskian non-Euclidean geometry. This fact, established in 1868 by E. Beltrami, was of great importance in the dispute over the reality of Lobachevskian geometry.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.