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


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.

Date Made: 1900-1914

Maker: Schilling, Martin

Location: Currently not on view

Place Made: Germany: Saxony, Leipzig

Subject: Mathematics


See more items in: Medicine and Science: Mathematics


Exhibition Location:

Data Source: National Museum of American History

Id Number: 1990.0571.09Catalog Number: 1990.0571.09Accession Number: 1990.0571

Object Name: Geometric Model

Physical Description: plaster (overall material)Measurements: overall: 20 cm x 19.2 cm x 12 cm; 7 7/8 in x 7 9/16 in x 4 23/32 in


Record Id: nmah_1213895

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