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Geometric Model, L. Brill No. 26. Carton Ser. No. 6, Hyperbolic Paraboloid Made from Cardstock

Geometric Model, L. Brill No. 26. Carton Ser. No. 6, Hyperbolic Paraboloid Made from Cardstock

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Description
In the nineteenth and early twentieth century, students studying technical subjects often learned about the representation of surfaces by equations in courses in solid analytic geometry. Schools in Europe, the United States, and Japan sometimes purchased models to illustrate such surfaces. The firm of Ludwig Brill in Darmstadt published this one as part of a series of paper models (the “Carton” series) designed by Alexander Brill and first issued in 1874. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
This tan paper model of a hyperbolic paraboloid consists of thirteen portions of triangles, intersecting portions of another thirteen triangles. It is stored flat in a gray envelope which in turn is in a brown paper box with the other models in the series. A mark stamped on the model reads: Verlag von L. Brill in Darmstadt.
The saddle-shaped surface is represented by the equation: + y2/ b2 - x2/a2 = -2z. Sections by any plane where x = c or y=c (c being an arbitrary constant) are parabolas. Sections parallel to the plane z = 0 are hyperbolas. The top edges of the pieces are straight lines, illustrating that the hyperbolic paraboloid is a ruled surface.
Compare MA.304723.669.
References:
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 1, 57.
Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, p. 243-244.
Location
Currently not on view
Object Name
geometric model
date made
1892
maker
L. Brill
place made
Germany: Hesse, Darmstadt
Physical Description
paper (overall material)
Measurements
overall: 10 cm x 14 cm x 8 cm; 3 15/16 in x 5 1/2 in x 3 5/32 in
ID Number
1985.0112.021
catalog number
1985.0112.021
accession number
1985.0112
Credit Line
Gift of Wesleyan University
subject
Mathematics
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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