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geometry.college.independent  Topic: 4D Visualization Replies: 9
  Last Post: Apr 8, 1994 10:36 AM  Advanced Search  Evelyn
Sander  Posts: 187 Registered: 12/3/04 4D Part 3: Minimal
Surfaces Posted: May 27, 1993 10:49 AM  Given a fixed boundary
in nD, what n-1 dimensional hypersurface with this boundary has
the minimum area? This is the question to answer in the field of
minimal surfaces, studied by Ken Brakke and John Sullivan of the
Geometry Center. In three dimensions, this question becomes:
given a boundary in 3D, such as a loop or shape made out of
wire, what is the surface with minimum area with this wire as
its boundary? The answer should be quite familiar to everyone;
the soap film formed by dipping a wire frame in soap solution
gives a surface of minimum area with that boundary.  Sometimes
these surfaces are unexpected. For example, a tetrahedral frame
makes a soap film with p