Geometric Model, L. Brill No. 8. Ser.3 No. 5, Hyperboloid of One Sheet

Geometric Model, L. Brill No. 8. Ser.3 No. 5, Hyperboloid of One Sheet

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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. 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 an elliptic hyperboloid of one sheet, a surface that can be represented by the equation x2/a2 + y2/ b2 - z2/c2 = 1. Here x and y are axes in the horizontal plane and z is the vertical axis. A plane cutting the surface parallel to the plane z = 0, and any plane parallel to it, produces an ellipse. Sections by the planes x = 0, y = 0, and planes parallel to these, are hyperbolas. A tag on the model reads: 8. Another tag reads: Einschaliges Hyperboloid. (/) Verl.... Brill 3. Ser. Nr. 5. Also marked on it are an ellipse (in the plane z = 0) and four sections of hyperbolas (in the planes x = 0 and y = 0).
The model is missing a section around the top.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 7, 58.
Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931.
Currently not on view
Object Name
geometric model
date made
L. Brill
place made
Germany: Hesse, Darmstadt
Physical Description
paper (overall material)
plaster (overall material)
overall: 23 cm x 23 cm x 12.5 cm; 9 1/16 in x 9 1/16 in x 4 29/32 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
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Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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