Geometric Model, L. Brill No. 91. Ser. 12 No. 1, Space Curve of Fourth Order

Geometric Model, L. Brill No. 91. Ser. 12 No. 1, Space Curve of Fourth Order

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This is one of four string models showing space curves of fourth order that were designed by the German mathematician Hermann Wiener (1857-1939) and first published by Ludwig Brill in 1884. The model has a metal frame painted black. The top of the frame has a small circle, the bottom a large one. Joining these with strings (all the strings of this example are missing) would produce a double cone. Joining other pieces on the top and sides would produce part of a double elliptic cone. Joining small ellipses on two opposite sides would produce an elliptic cylinder, considered as another form of cone. Joining opposites hyperbolic arcs would produce a hyperbolic cylinder, treated here as a fourth cone. Hence the model is considered as consisting of four real cones, with lines of intersection marked by beads representing a space curve of fourth order. This example of the model has no tag.
This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It came to the Smithsonian from Wesleyan University in 1985.
L. Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 24, 74.
There is an example of the model, produced slightly later by Martin Schilling and having strings, at the University of Utrecht. It is shown on the website This website was accessed August 18, 2020.
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: 32.7 cm x 32 cm x 32 cm; 12 7/8 in x 12 19/32 in x 12 19/32 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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