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B3D Cover

This was used as the cover image for Tom Banchoff's book Beyond the Third Dimension, part of the Scientific American Science Library. Here again, we see a view of a torus projected from four-space into three-space, similar to the one appearing in In- and Outside the Torus. This time, however, the bands are not Hopf circles, and the viewpoint is one from a sequence of views as the torus rotates in four-space (another is the rotus of revolution shown in Banded Torus). As it rotates, the projected torus "turns inside out", and the circles change from going around the tube to going around the hole. The view shown here is not quite to where the projection point is on the torus (where the projection extends to infinity as it turns inside out).

The complete sequence is shown in one of the animations on the home page for the TFBCON, and as part of the virtual art exhibit Surfaces Beyond the Third Dimension.

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Created: 13 Oct 2003
Last modified: Oct 13, 2003 10:26:33 PM
Comments to: dpvc@union.edu
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