Half the Surface of Revolution generated by a Tractrix about its Asymptote to form a Tractroid.
The Cartesian parametric equations are

(1) | |||

(2) | |||

(3) |

for .

It has constant Negative Curvature, and so is called a pseudosphere by analogy with the Sphere, which
has constant Positive curvature. An equation for the Geodesics is

(4) |

**References**

Fischer, G. (Ed.). Plate 82 in
*Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume.* Braunschweig, Germany: Vieweg, p. 77, 1986.

Geometry Center. ``The Pseudosphere.'' http://www.geom.umn.edu/zoo/diffgeom/pseudosphere/.

Gray, A. *Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 383-384, 1993.

© 1996-9

1999-05-26