Geometric Model, L. Brill No. 23. Ser. 3 No. 13, Hyperbolic Paraboloid

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 saddle-shaped plaster model shows a hyperbolic paraboloid. The surface is represented by the equation: + y²/ b² - x²/a² = - 2z. Sections by any plane where x = c or y=c (c being an arbitrary constant) are parabolas. Sections parallel to the plane z = 0 are hyperbolas. One hyperbola and one parabola both of which pass through the center of the surface, are shown on the model.

A paper tag near the base of the model reads: 23. Another paper tag reads: Hyperbolishes Paraboloid. (/) Verl. v. L. Brill 3 Ser. Nr. [...].

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. 243-244. An example of a related Brill model, with more lines of intersection shown on it, is shown as Figure 5.