Friday, July 2, 2010

Steiner Trees and Minimal Surfaces

There is a physical analog to the Steiner Tree Problem that allows one to find the solutions without doing a single calculation. The soap films of a wire frame model will form a minimal surface. If one uses the positions of a set of parallel wires in the frame to represent the points and eliminates the unwanted surfaces of the bubbles produced by dipping the frame in a soap solution, a set of minimal surfaces will be formed which is analogous to the Steiner tree. The analogy is even better if one looks just at a plane perpendicular to the parallel wires. See Soap Bubbles by C.V. Boys for more information about soap bubbles on wire frames.

Bubble Kits

Bubble Science Kit - Amazon

Bubble Science Kit - Target

Bubble Builder - Scientifics

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