Paper Model of a Hyperboloid of Two Sheets, M. Schilling No. 24, Carton Ser. No. 4

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

This blue paper model of a hyperboloid of two sheets consists of two parts, each of which have the dimensions given when unfolded. The parts consist of 22 circles and portions of circles. Each represents half of a hyperboloid. The two smallest circles are missing from both models. The lines of intersection are numbered, as are the circles. The two parts are stored in light green paper envelopes which each measure: 17.1 cm. w. x 11.5 cm. d. x .3 cm. h. The envelopes are stored in a black paper box with the other Carton models. A mark on the model reads: Karton-Modelle (/) von Flachen zweiter Ordnung. (/) Nr. 4. (/) Zweichaliges Hyperboloid. (/) Verlag von Martin Schilling in Halle a. S.; Leipzig.

The models together show part of a hyperboloid of two sheets, a surface that can be represented by the equation x²/a² + y²/ b² - z²/c² = - 1.

The stand for the model is part of MA.304722.24.

For a related model, made by Schilling’s predecessor Brill, see 1985.0112.014.

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.

Martin Schilling, Catalog mathematixsher Modelle, , ,, Leipzig, 1911, p. 1-2, 114.

Currently not on view