**The Pseudosphere**

by Andrea Mantler.

Last update = May 14, 98.

The **pseudosphere** is a surface of constant negative curvature. It is a model of the hyperbolic plane. This program allows the user to construct pseudospheres of various resolutions, and to view them from various angles, to place points on the surface, and to connect the points with lines (ie, geodesics in the pseudosphere).

**SGeometry** is a Power Macintosh program written by Andrea Mantler to display the pseudosphere. Click to download it.

When creating a pseudosphere there are two main parameters:

- theta is the angle of rotation about the axis.
- u parametrizes length along the axis.

The surface is represented as a large number of polygons, using 3D graphics. The pseudosphere looks best with thousands of colours or more. Do not use 256 colours.

Use the numeric keypad to rotate and zoom the pseudosphere.

Lines on the pseudosphere are geodesics that start at the edge, move outwards, and eventually return to the edge, usually circling the axis one or more times. Only lines parallel to the axis go to infinity.

A sample screenshot is shown below.

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