from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A surface generated by rotating a tractrix about its asymptote; a tractricoid
  • n. Any of various surfaces with constant negative Gaussian curvature.

from the GNU version of the Collaborative International Dictionary of English

  • n. 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.

from The Century Dictionary and Cyclopedia

  • n. A surface of constant negative curvature.
  • n. A sphere in non-Euclidean geometry.
  • n. The surface generated by the revolution of the tractrix about its asymptote.


from Wiktionary, Creative Commons Attribution/Share-Alike License

pseudo- +‎ sphere


  • University of California, Irvine, imagines a "pseudosphere" called Kuen's surface as an equation, a drawing, and a glass sculpture.

    National Geographic News

  • Diagram of pseudosphere, from MacTutor History site.

    Hermann von Helmholtz

  • A rash of small red lights appeared in the darkness above the section of pseudosphere.


  • Euclid's fifth postulate, that two straight -- i.e. geodetic -- lines intersect when the sum of the interior angles is less than two right angles, does not hold for geometry on the pseudosphere.

    The Fourth Dimension Simply Explained

  • The shortlist is completed by The Changing World of Inflammatory Bowel Disease and Crocheting Adventures with Hyperbolic Planes, which informs its readers how to "crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids", as well as exploring geometry and its historical connections with art, architecture, navigation and motion, and the history of crochet.

    Culture |


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