Geometry of the Hopf Mapping and Pinkall's Tori of Given Conformal Type
by Thomas F. Banchoff

The Hopf mapping from the 3-sphere to the 2-sphere and its investigation using computer graphics were discussed at the Conference on Computers in Geometry and Topology. Ulrich Pinkall gave a presentation in which he determined the conformal structure of tori obtained by lifting a closed curve on the 2-sphere under the Hopf mapping. This paper is a discussion of Pinkall's results, and it is an excellent example of a problem for which computer graphics are useful.