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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. These objects are 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.
The plaster model shows a hyperboloid of two sheets. The surface can be represented by the equation x2/a2 + y2/ b2 + z2/c2 = - 1. Sections parallel to the plane z=0 are ellipses. Sections by the planes x=0 and y=0, and planes parallel to these, are hyperbolas. Two metal rods hold together the two sheets.
Grids of perpendicular lines of curvature are shown. A paper tag on the model reads: Zweischaliges Hyperboloid. (/) 3. Ser., Nr. 9. (/) Verlag v. Martin Schilling, Leipzig.
Ludwig Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 7, 77.
Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 240-241.
Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 62, vol. II, pp.25-28.
Currently not on view
Germany: Saxony, Leipzig
plaster (overall material)
iron (overall material)
overall: 23.8 cm x 21.8 cm x 12.8 cm; 9 3/8 in x 8 19/32 in x 5 1/32 in