Wire model – Soap Film Minimal Surface, ca 1892, Smithsonian Institution negative number NMAHAHB2017q018046

Particularly in the mid-19th century, mathematicians and physicists explored the mathematical properties of soap films. Ideally, the surface formed when a closed wire frame is dipped in soapy water is a minimal surface, that is to say the surface of smallest area of all the surfaces bounded by the frame. This example has two circular rings, one of which sits atop the other. The surface formed by the soap is a catenoid. The model was one of a set designed by students of German mathematician Alexander Brill (1842–1935) and manufactured by his brother Ludwig Brill of Darmstadt. This example was exhibited at the World’s Fair of 1893, held in Chicago.

Images of a series of such models by Brill, with appropriate films, may be examined at https://americanhistory.si.edu/collections/object-groups/geometric-models-minimal-surfaces-as-soap-films.