Paper Model of a Hyperboloid of One Sheet, M. Schilling No. 13, Carton Ser. No. 3

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 Martin Schilling published this one as part of a series of paper models (the “Carton” series) designed by Alexander Brill and first issued in 1874.

This pink paper model of a hyperboloid of one sheet has the dimensions given when unfolded. It measures flat in its light green paper envelope: 17 cm. w. x 11.5 cm. d. It is composed of thirty-four circles and segments of circles. The lines of intersection are numbered, but there are no maker's marks on the model. The envelope is stored in a black paper box with the other Carton models. The envelope is in a brown box with the other models in the Carton series. A tag on the envelope reads: Karton-Modelle (/) von Flachen zweiter Ordnung. (/) Nr. 3. (/) Einschaliges Hyperboloid. (/) Verlag von Martin Schilling in Halle a. S. another mark there reads: Leipzig.

The model shows a 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 MA.304722.24.

Compare 1985.0112.007

References:

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

M. Schilling, Catalog, 1911, p. 1-2, 112.

Currently not on view