Geometric Model, M. Schilling No. 190 or L. Brill No. 101. Ser. 3 No. 16, Hyperbolic Paraboloid

Geometric Model, M. Schilling No. 190 or L. Brill No. 101. Ser. 3 No. 16, 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 or its successor, Martin Schilling in Leipzig.
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 parts of parabolas. Sections parallel to the plane z = 0 are parts of hyperbolas. A grid of perpendicular lines of curvature is shown on the model.
A tag on the model reads: 3. Ser. Nr. 16. The use of the abbreviation "Ser." (and not "Serie") on the label suggests that the model was sold by Brill and not Schilling.
Compare 1985.0571.15 and 1985.0112.74.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 7, 77.
Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. II, pp.25-28.
Currently not on view
Object Name
Geometric Model
date made
place made
Physical Description
plaster (overall material)
overall: 12 cm x 15.8 cm x 15.8 cm; 4 23/32 in x 6 7/32 in x 6 7/32 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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