Geometric Model, L. Brill No. 148. Ser. 10 No. 1a, Minimal Surface in Two Parts

Geometric Model, L. Brill No. 148. Ser. 10 No. 1a, Minimal Surface in Two Parts

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Students at the technical high school in Munich, working under the direction of Alexander Brill, developed a series of wire models of minimal surfaces that was first published by Ludwig Brill in 1885. 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 are often represented by soap films, as was the intention with this model.
This, the first model in the series, is in two parts. One is a wire circle with three wire supports and the second circle of the same diameter with a handle. If the circles are held together, a soap film spans both of them. Separating the circles produces a film in the shape of a catenoid and then, when the circles are separated further, circles span the two discs separately.
This example was exhibited at the Columbian Exposition, a world's fair held in Chicago in 1893.
L. Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill,1892, p. 21, 85.
G. Fischer, Mathematical Models: Commentary, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 41-43.
A. T. Fomenko, The Plateau Problem, Part I, Historical Survey, New York: Gordon and Breach, 1990, pp. 22-34.
J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires, vol. 1, Paris: Gauthier-Villars, 1873, pp. 93-103. This work is mentioned in the Brill catalog.
Currently not on view
Object Name
geometric model
geometric model
date made
L. Brill
place made
Germany: Hesse, Darmstadt
Physical Description
metal (overall material)
overall: 7.2 cm x 8 cm x 8 cm; 2 27/32 in x 3 5/32 in x 3 5/32 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
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Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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