Geometric Model, L. Brill No. 97. Ser. 3 No. 7, 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. These objects are 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.
This plaster model shows a hyperboloid of one sheet with an elliptic base and top. The surface can be represented by the equation x2/a2 + y2/ b2 - z2/c2 = 1. Sections by the planes x=0 and y=0, and planes parallel to these, are hyperbolas. Section by planes z = k, parallel to the plane z=0, are similar ellipses. A grid of orthogonal lines of curvature is shown on the model. A paper tag on it reads: Einschaliges Hyperboloid. (/) Verl. v. L. Brill. 3. Ser. Nr. 7.
Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 64, vol. II, pp.25-28.
Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 7, 76.
Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 239-240. An example of this model is shown in Figure 2.
Currently not on view
date made
L. Brill
place made
Deutschland: Hessen, Darmstadt
Physical Description
paper (overall material)
plaster (overall material)
overall: 23.3 cm x 23 cm x 13.3 cm; 9 3/16 in x 9 1/16 in x 5 1/4 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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