Saturday, July 10, 2010

Pentagon Soap Films

I made a wire frame pentagon using #14 copper wire, some styrofoam packing material as a base and some hot glue to hold everything together. Using the styrofoam packing material allows more freedom in the position of the parallel wires. Ordinary dish washing detergent in a large pot was used to create the soap films. One has to dip the frame upside down in order to form the Steiner tree. Right side up produces only five parallel sheets along the perimeter.

The two lower side sheets which connect with the lower base sheet have a curved intersection which drops away from the upper level of the pentagon. If one looks closely one can see where these sheets intersect with the styrofoam at the bottom. The tree produced is very close to what was computed. The surface tension may have caused the soap films to adapt to balance the forces on them.

One has to be quick to capture these films with a weak soap solution. I had to hold the camera in one hand and dip the wire frame with the other. It took several attempts and a little coordination to successfully capture the trees before they disappeared.

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