SB3D (Tour/Triple)

# Movies of the Triple-Point Twist

This movie shows the triple-point surface rotating in space. You can see the Triple-Point from various angles. Several views similar to these appeared as chapter headings in the book Statistics: The Conceptual Approach by Iverson and Gergen.

Here, the surface is pulled apart so that the triple point is removed. The parameterization of the surface has a constant c that varies from -1 to 1 in this movie. At c = 0, the singularity disappears and the surface becomes embedded.

The triple-point surface is a ruled surface, meaning that is can be swept out by a line moving over time. In this movie, we see this line as it generates the surface. The line first sweeps out a portion of the surface, then seems to backtrack, causing the surface to intersect itself. Finally, it curves back on itself a third time, and passes through the curve of self-intersection again, forming the triple point.

See the description of movie formats and plug-ins if you are having difficulty getting these movies to play.

 Surfaces Beyond the Third Dimension Last modified: 08 Oct 2000 09:31:58 Comments to: Thomas F. Banchoff (`thomas_banchoff@brown.edu`)