Geometric Model by L. Brill, No. 225, Ser. 18 No. 3, Ruled Surface of Third Degree

Geometric Model by L. Brill, No. 225, Ser. 18 No. 3, Ruled Surface of Third Degree

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This is one of a set of four models of ruled surfaces originally published by Ludwig Brill in 1891. The series was designed by C. Tesch, an assistant to Christian Wiener (1826-1896), a professor at the technical high school in Karlsruhe. Tesch also designed Series 20 of Brill’s models (also published in 1891) and, after graduation, Series 22 (published in 1894, by which time Tesch is listed as an engineer with no academic affiliation).
This, the third model in Brill's Series 18, has a black metal frame and red and green threads, with gold beads. The three sides are roughly straight, with complex curves on the top and bottom. One side is broken off. The threads in this example are presently broken.
All the models in the series are meant to show ruled surfaces of degree three. As in #2, there should be two lines of intersection of the ruled surfaces, marked by beads, but these lines would meet only infinitely far from the model.
This example of the model was exhibited at the Columbian Exposition, a World’s fair held in Chicago in 1893.
Compare 1985.0112.179.
L. Brill, Catalog, 1892, p. 64-65, 44-45.
Richter, K., Online Collection of Mathematical Models, Martin-Luther-Universität Halle-Wittenberg. This collection has the web address: The example of this model shown there has number A3-032 in that collection.
Tesch. C., Modelle der Regelfaechen dritten Gerades. A copy of this essay, which gives a brief historical account of the development of the model at Karlsruhe, is online at It was posted in connection with the copy of the model at the University of Goettingen (their model 74).
Currently not on view
Object Name
geometric model
geometric model
date made
L. Brill
place made
Germany: Hesse, Darmstadt
Physical Description
string (overall material)
glass (overall material)
metal (overall material)
overall: 21.6 cm x 20.5 cm x 20.5 cm; 8 1/2 in x 8 1/16 in x 8 1/16 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
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Medicine and Science: Mathematics
Data Source
National Museum of American History
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