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Geometric Model, M. Schilling No. 189. Ser. 3 No. 12, Elliptic Paraboloid

Geometric Model, M. Schilling No. 189. Ser. 3 No. 12, Elliptic 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.
The plaster model shows an elliptic paraboloid. The surface is represented by the equation: x2/a2 + y2/ b2 = -2z. The apex of the surface is at the origin (so that all the values of z are negative). Sections by the planes x = 0 and y = 0, as well as by planes parallel to them, are parabolas. Sections parallel to and below the plane z = 0 are ellipses that increase in size going downward. A grid of orthogonal curves is indicated on the model.
A tag on the model reads: Elliptisches Paraboloid. (/) 3. Serie, Nr. 12 (/) Verlag v. Martin Schilling, Leipzig
Compare 1985.0112.015, 1985.0112.016, and 1985.0112.017. Also compare 1990.0571.10.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 7, 77.
Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 61, vol. II, pp.25-28.
Martin Schilling, Catalog, 1911, pp. 7-8, 138.
Currently not on view
Object Name
Geometric Model
date made
Schilling, Martin
place made
Germany: Saxony, Leipzig
Physical Description
plaster (overall material)
overall: 20 cm x 19.3 cm x 12 cm; 7 7/8 in x 7 19/32 in x 4 23/32 in
ID Number
catalog number
accession number
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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