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Movies of the Triple-Point Twist

[Rotating Surface]

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.

[Removing the Triple-Point]

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.

[Sweeping Out the Surface]

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
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