Sunday, July 11, 2010

"Minimal Surfaces" a Misnomer?

Here is a side view of the soap films for the pentagonal frame. It looks like all the film intersections are curved lines as can be seen in the two nearer vertical intersections. The soap films do not appear to be minimal surfaces as claimed but may more correctly be called equilibrium surfaces. The stresses and forces in the films have to balance out everywhere. The films themselves are subject to gravitational forces and the intersections dropping from the vertices of the pentagon look similar to catenaries. Pressure changes are negligible except for the spherical bubble in the background. Internal stresses in the films are probably not uniform due to the weight of the films as one finds for the tension in a hanging string.

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