Geometric Models - Minimal Surfaces as Soap Films

A minimal surface is the surface of smallest area of all the surfaces bounded by a closed curve in space. Its mean curvature is zero. Minimal surfaces greatly interested a few nineteenth century physicists and mathematicians, fascinated by their connection to soap films. In the 1880s, students at the technical high school in Munich, Germany, under the direction of their professor, Alexander Brill, designed a series of wire models that, when dunked in appropriate soapy water, produced intriguing surfaces.

Brill arranged that these and other mathematical models be manufactured and distributed by his brother Ludwig Brill. Examples were exhibited at the world’s fair held in Chicago in 1893. These and the other Brill models shown at the fair were purchased by Wesleyan University, which later donated them to the Smithsonian. The mathematics associated with soap films continues to fascinate both scholars and the general public.


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