Geometric Model, M. Schilling No. 33. Ser. 3 No. 14, Hyperbolic Paraboloid

Geometric Model, M. Schilling No. 33. Ser. 3 No. 14, Hyperbolic Paraboloid

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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. This object is part of series of models of quadric surfaces (surfaces of degree two) designed in 1878 by Rudolf Diesel, then a student at the technical high school in Munich. It was published by the firm of Ludwig Brill in Darmstadt and by his successor Martin Schilling – this is Schilling’s version of the model.
The saddle-shaped plaster model shows a hyperbolic paraboloid. The 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. One hyperbola and one parabola both of which pass through the center of the surface, are shown on the model. Also shown are various planar cuts in the form of hyperbolas.
A paper tag on the model reads: [...] rbolishes Paraboloid. (/) 3. Serie, Nr. 14. (/) [...] v. Martin Schilling, Leipzig.
For a version of this model published by Schilling’s predecessor, Ludwig Brill, see 1990.0571.12.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 7, 59.
Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, p. 243-244, Figure 5
M. Schilling, Catalog, 1911, p. 7, 114.
Currently not on view
Object Name
Geometric Model
date made
Schilling, Martin
place made
Germany: Saxony, Leipzig
Physical Description
plaster (overall material)
overall: 12 cm x 15.4 cm x 15.4 cm; 4 23/32 in x 6 1/16 in x 6 1/16 in
ID Number
catalog number
accession number
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Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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