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# Geometric Model, L. Brill No. 21. Ser. 3 No. 11, Elliptic Paraboloid

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Description
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. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
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 at the front reads: Elliptisches Paraboloid. (/) Verl. v. L. Brill. 3 Ser. Nr. 11.
Compare 1985.0112.015 , 1985.0112.016, and 1985.0112.017.
References:
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. An example of this Brill model is shown as Figure 4.
Location
Currently not on view
Object Name
geometric model
1892
maker
L. Brill
Physical Description
paper (overall material)
plaster (overall material)
Measurements
overall: 20 cm x 19 cm x 12 cm; 7 7/8 in x 7 15/32 in x 4 23/32 in
ID Number
1985.0112.016
catalog number
1985.0112.016
accession number
1985.0112
Credit Line
subject
Mathematics
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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