Keys to Mathematical Treasure Chests: 19th-century String Models – Later Makers of String Models

The relatively simple paper models made by Jullien generally show the projection of a few line segments onto perpendicular planes. Some model makers continued the tradition of making more elaborate ruled surfaces, although they generally described them as mathematical (rather than engineering) models. Those distributed most widely were made and sold by the Germans Ludwig Brill and his successor Martin Schilling. Examples of these survive in collections across the world. About twenty are in the Smithsonian’s National Museum of American History (NMAH), most from a collection of Brill models exhibited at the World’s Fair held in Chicago in 1893. Brill's successor, Martin Schilling, would continue to sell these models well into the 20th century.

For examples of Brill models of ruled surfaces in the Smithsonian collections, see https://americanhistory.si.edu/collections/search?return_all=1&edan_local=1&edan_q=Brill%20%22ruled%20surface%22%20metal%20Wesleyan. This chest has an extra treasure!

Figure 5. Brill’s model of a hyperbolic paraboloid, 1892. Smithsonian Institution negative number NMAH-97-9530.

American model makers such as the firm of Eberbach in Ann Arbor, Michigan, and University of Iowa professor Richard P. Baker made similar models in the late 19th and early 20th centuries—examples of these also survive at the Smithsonian and, in Baker’s case, at the University of Arizona. Baker distributed his models into the 1930s.

For two Eberbach models of ruled surfaces, see https://americanhistory.si.edu/collections/search/object/nmah_1213977 and https://americanhistory.si.edu/collections/search/object/nmah_1196291. Two related, unsigned models from the University of Michigan are https://americanhistory.si.edu/collections/search/object/nmah_1213978 and https://americanhistory.si.edu/collections/search/object/nmah_213480.

For Baker’s string models of ruled surfaces, see https://americanhistory.si.edu/collections/search?return_all=1&edan_local=1&edan_q=Baker%20ruled%20surface&. Examples of Baker models of ruled surfaces are also found at the University of Arizona. See Mathematical Models at the University of Arizona, particularly under “Ruled surfaces.” Not all of the ruled surfaces shown at this address are by Baker.