Geometric Model, L. Brill No. 148 (?). Ser. 10 No. 1i?, Minimal Surface

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. It is one of a series. The model is in the shape of a rhombus, bent along a diagonal. A handle rises from one of the corners not at the bend. Either model 1985.0112.114 or model 1985.112.115 may be Brill Ser. 10 No. 1i. That model was designed to illustrate one of the surfaces proposed by the German mathematician Heinrich Scherk (1798-1885) in a paper of 1835.

This example was exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893.

References:

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.

Scherk, H.F., “Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen,” Journal fuer die reine und angewandte Mathematik, 13, 1835, pp. 185-208. This article is mentioned in the Brill catalog.

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