Geometric Model, M. Schilling No. 27. Ser 3 No. 11, Elliptic Paraboloid

Geometric Model, M. Schilling No. 27. Ser 3 No. 11, 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 its successor, Martin Schilling in Leipzig.
The plaster model shows 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.
This model has twelve ellipses on it, parallel to the base. A tag reads: Elliptisches Paraboloid. (/) 3. Serie, Nr. 11 (/) Verlag v. Martin Schilling, Leipzig
Compare 1985.0112.015, 1985.0112.016, 1985.0112.017, 1990.0517.08, and 1990.0571.09.
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. 242, Figure 4.
Martin Schilling, Catalog mathematischer Modelle..., Leipzig, 1911, p. 7-8, 114.
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 19.2 cm x 12 cm; 7 7/8 in x 7 9/16 in x 4 23/32 in
ID Number
catalog number
accession number
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Medicine and Science: Mathematics
Data Source
National Museum of American History
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