Geometric Model, L. Brill No. 21 or M. Schilling No. 27. Ser 3 No. 11, Elliptic Paraboloid
date: label: date made
content: 1880-1914
notes: label: Description
content: 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.
label: Description
content: The plaster model shows elliptic paraboloid. The surface is represented by the equation: x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/ b<sup>2</sup> = -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. Two such parabolas are roughly drawn in light blue on the model. Sections parallel to and below the plane z = 0 are ellipses that increase in size going downward.
label: Description
content: This model has twelve ellipses on it, parallel to the base. It has no tags, although various initials are carved in the base.
label: Description
content: Compare 1985.0112.015, 1985.0112.016, 1985.0112.017, 1990.0517.08, and 1990.0571.09.
label: Description
content: References:
label: Description
content: Ludwig Brill, <I>Catalog mathematischer Modelle. . .<I>, Darmstadt: L. Brill, 1892, p. 7, 59.
label: Description
content: Henry Burchard Fine and Henry Dallas Thompson, <I>Coordinate Geometry</I>, New York: Macmillan Company, 1931, p. 242, Figure 4.
label: Description
content: Martin Schilling, <I>Catalog mathematischer Modelle. . .</I>, Leipzig, 1911, p. 7-8, 114.
label: Location
content: Currently not on view
place: label: place made
content: Germany
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1990.0571.08
label: catalog number
content: 1990.0571.08
label: accession number
content: 1990.0571
objectType: label: Object Name
content: Geometric Model
physicalDescription: label: Physical Description
content: plaster (overall material)
label: Measurements
content: overall: 20 cm x 19.2 cm x 12 cm; 7 7/8 in x 7 9/16 in x 4 23/32 in