Visualizing Soap Film Minimal
Surfaces on Knots
Nathaniel Friedman
Department of Mathematics
University at Albany
A knot diagram can be considered as a map that can
be two-colored shaded and white(checker boarding). If a wire model of the knot
diagram is dipped in a soap solution, the resulting soap film minimal surface
(sfms) will correspond to the shaded regions, whereas the white regions will
be disks that are punctured to obtain "windows". Thus the checker boarding of
the knot diagram predicts the surface and windows of the sfms. If the shaded
regions can be colored red and blue so that the colors switch at every
crossing, then the sfms is two-sided. Otherwise, the sfms is one-sided.