Geometric Model, L. Brill No. 18, Carton Ser. No. 4 - Half of a Hyperboloid of Two Sheets

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. The firm of Ludwig Brill in Darmstadt published this one as part of a series of paper models (the “Carton” series) designed by Alexander Brill and first issued in 1874. 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 tan paper model of one sheet of a hyperboloid of two sheets consists of portions of twelve circles intersecting portions of twelve other circles. It is in a gray paper envelope which also contains model 1985.112.001. The envelope is in a brown box with the other models in the Carton series. A mark on the model reads: Verlag von L. Brill in Darmstadt.

The surface shown can be represented by the equation x²/a² + y²/ b² - z²/c² = - 1. It is displayed on a stand that is part of 1985.0112.005.

References:

Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 1, 59.

Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 240-241.

Currently not on view