Geometric Model, L. Brill No. 10. Carton Ser. No. 3, Hyperboloid of One Sheet

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. 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 particular 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 orange paper model of a one-sheeted hyperboloid consists of portions of seventeen circles intersecting portions of seventeen other circles. A mark stamped on the object reads: Verlag von L. Brill in Darmstadt. The model is in a gray paper envelope which also contains model 1985.112.003. The envelope is in a brown box with the other models in the Carton series.

The model shows an hyperboloid of one sheet, a surface that can be represented by the equation x²/a² + y²/ b² - z²/c² = 1. Here z is a horizontal axis, with the x and y-axes perpendicular to it. The model is displayed on a stand that is part of 1985.0112.005.

Reference:

L. Brill, Catalog, 1892, p. 1, 59.