SB3D (Tour/Torus)

The last image featured in the exhibit is an interior view of a cyclide of Dupin, a torus on a three-dimensional sphere in four-space projected stereographically from a point on the torus itself, leading to a third-order algebraic surface expressed as a union of circles (and four straight lines). These curves are orbits of a Hamiltonian dynamical system and the fibers over a great circle of the Hopf mapping from the three-sphere to the two-sphere. The exhibit booklet and the electronic links refer the viewer to several articles written by the author and colleagues in Applied Mathematics and Computer Science, examining different aspects of this extremely important surface. This image is also featured on the cover of the Scientific American Library volume Beyond the Third Dimension.

Surfaces Beyond the Third Dimension Last modified: 08 Oct 2000 08:18:59 Comments to: Thomas F. Banchoff (thomas_banchoff@brown.edu)

The Mathematics of In- and Outside the Torus In- and outside the Torus