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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 https://www.uu.nl/en/research/3d-geometric-models/schilling-1201. This website was accessed August 18, 2020.
Currently not on view
geometric model; Space Curve of Fourth Order
Germany: Hesse, Darmstadt
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