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Artist's Comments on the Triple Point Twist

This is one of the most elaborate entries in the exhibit, not because of the complexity of the image but because of the linkages. "Triple-Point Twist" appeared in slightly rotated form on the cover of the Notices of the AMS, as well as on the cover of a statistics volume by Iversen and Gergen [Statistics: The Conceptual Approach]. As chapter headings in that latter volume there were fourteen views of this object rotating in three-space. These can be accessed in the virtual exhibit either as an MPEG movie or as a virtual reality VRML document, enabling the viewer of the electronic version to interact with the object in ways impossible for the gallery visitor.

Even more significant than watching the object rotate is to view and review an MPEG movie that makes the object unfold, changing one of the parameters that twist the "bamboo curtain" ruled surface so that it intersects itself, forming a triple point. The equations defining the surface have been studied extensively by David Mond and Washington Marar.

It is these enhancements that represent the true innovation in such a virtual gallery. The viewer who becomes fascinated by one or another of the aspects of an object can investigate them at different levels, depending on the background and interests of the individual. In particular, it is possible in some cases to view and manipulate phenomena that relate the particular object to a wider area of mathematics.