Geometric Model, M. Schilling No. 187. Ser. 3 No. 18, Elliptic Cone

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 model 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. They were published by the firm of Ludwig Brill in Darmstadt and by Brill’s successor, Martin Schilling – this is Schilling’s version. The model shows an elliptic cone. The surface can be represented by the equation x²/a² + y²/ b² - z²/c² = 0. Here x and y are axes in the horizontal plane and z is the vertical axis. Assuming that z=0 at the apex of the cone, a plane cutting the surface parallel to the plane z = 0 produces an ellipse. The model is marked with a system of perpendicular lines of curvature. A paper tag on it reads: Elliptischer Kegel. (/) 3. Serie, Nr. 18. (/) Verlag v. Martin Schilling, Leipzig

For Brill's version of the model, see 1990.0571.16 and 1985.0112.071.

References:

Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 7, 76.

Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 63, vol. II, pp.25-28.

M. Schilling, Catalog, 1911, p. 7-8, 138.