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In 1880, Ernst Lange, a student at the mathematical institute of the technical high school in Munich, working under the direction of Felix Klein, designed four plaster models of space curves of degree three drawn on cylinders with cross sections that were conic sections. All of these curves represented the intersection of a surface of degree two with the cylinder shown.
This model, the first in the series, shows the intersection of a cone with an elliptic cylinder. The curve of intersection, called a cubic ellipse, is incised on the model. A paper tag on the model reads: Raumcurve 3. Ordnung. (/) Verl. v. L. Brill. 6. Ser. Nr. XIXa.
Compare 1985.0112.061, 1990.0571.24, and 1990.0571.25. For another curve drawn on an elliptic cylinder, see 1982.0795.32
L. Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill,1892, p. 13, 73-74.
E. Lange, Mathematische Modelle XIX. Die vier Arten der Raumcurven dritter Ordnung, pp. 1-2. A copy of this document is available online through the website of the Göttingen collection of mathematical models. Accessed November 13, 2017.
Mathematics Institute of Oxford University website. This indicates that the intersecting surfaces are an elliptic cylinder and a hyperbolic parabola.
Ulf Hashagen, Walther von Dyck (1856-1934): Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart: Franz Steiner, 2003, p. 90, 100, 102.
Currently not on view
geometric model; Third Order Space Curve
Germany: Hesse, Darmstadt
plaster (overall material)
paper (overall material)
overall: 10.4 cm x 8 cm x 5 cm; 4 3/32 in x 3 5/32 in x 1 31/32 in