Geometric Model, L. Brill No. 13. Ser. 4 No. 3, Moveable Hyperboloids of One Sheet (Ruled Surfaces)

Geometric Model, L. Brill No. 13. Ser. 4 No. 3, Moveable Hyperboloids of One Sheet (Ruled Surfaces)

<< >>
Usage conditions apply
From the early nineteenth century, mathematicians and engineers have studied surfaces generated by motion. In a complete form of this model, two sets of threads join the small circle (with its tangent line) at the top and the larger circle (with its tangent line) toward the bottom.
One set of threads forms a cone and its tangent plane. The threads within it form a double cone. If the circle at the top or bottom is rotated, the tangent plane becomes a hyperbolic paraboloid and the double cone and outside cone become two different hyperboloids.
Compare to model 1985.0112.009 (Brill’s Ser. 4, No. 2), in which the two metal circles are equal and the outer curve is a cylinder.
This German model of a surface of second order is one of a series of five first introduced by Brill in 1879, rather early in the life of the company. This example was exhibited at the Columbian Exposition, the world's fair held in Chicago in 1893. It came to the Smithsonian from the mathematics department of Wesleyan University in Connecticut. It presently lacks weights and the strings are broken.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 9-10, 58-59.
Currently not on view
Object Name
geometric model
date made
L. Brill
place made
Germany: Hesse, Darmstadt
Physical Description
string (overall material)
glass (overall material)
metal (overall material)
overall: 52.5 cm x 33.7 cm x 16 cm; 20 21/32 in x 13 9/32 in x 6 5/16 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
Nominate this object for photography.   

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.


Add a comment about this object