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.

• MPEG version (204K)
• QuickTime version (314K)
• Animated GIF (1M)

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.

• MPEG version (153K)
• QuickTime version (240K)
• Animated GIF (996K)

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.

• MPEG version (207K)
• QuickTime version (302K)
• Animated GIF (825K)