Geometric Model, L. Brill No. 148 . Ser. 10 No. 1b, 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. This, the second model in the series, has a straight vertical axis with a spiral on the outside. The form of the soap film is a helicoid.

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.

J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires , vol. 1, Paris: Gauthier-Villars, 1873, pp. 216-217. This work is mentioned in the Brill catalog.

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