You are here

Mathematical Treasure: Model for Soap Film Minimal Surface by Brill

Author(s): 
Peggy Aldrich Kidwell (National Museum of American History, Smithsonian Institution)

Wire model by Brill for demonstrating a minimal surface made by soap film, circa 1892.

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.

Index of Mathematical Treasures

Index of Mathematical Objects

Peggy Aldrich Kidwell (National Museum of American History, Smithsonian Institution), "Mathematical Treasure: Model for Soap Film Minimal Surface by Brill," Convergence (May 2021)

Mathematical Treasures: Smithsonian National Museum of American History Object Groups