Good candidates for least area soap films
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Soap films are presented as potential global area minimizers subject to a topological constraint. Experimentally, this constraint is the shape of the soapy water in a soap film experiment. In this context, soap films which are probable area minimizers for rectangular n-prisms are described. By allowing area minimizers which arise as deformations of higher genus surfaces, we are able to discover previously unknown soap films spanning rectangular n-prisms with large aspect ratios and n ≥ 5. For n = 3, 4, 5, we show that the central film contracts to a point as the aspect ratio of the prism increases. We also prove that the area of the central hexagon for a soap film spanning a tall 6-prism approaches zero like (height)−4 as the height approaches infinity, provided we fix the length of the hexagon base. Finally, we prove that, if the aspect ratio is large enough, the soap film produced experimentally spanning a 4-prism has films which look planar but in reality are non-planar.
KeywordsSoap film Experiment Least area Rectangular prism
Mathematics Subject ClassificationPrimary 49Q05 Secondary 51M04
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