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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.