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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. The firm of Martin 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.
The tan paper model of an elliptic paraboloid consists of 26 intersecting circles and portions of circles. The two smallest circles are missing. The lines of intersection are numbered. The model is stored in light green paper envelope. The envelope is in a black paper box with the other models in the Carton series. A mark on the envelope reads: Karton-Modelle (/) von Flachen zweiter Ordnung. (/) Nr. 5. (/) Elliptisches Paraboloid. (/) Verlag von Martin Schilling in Halle a. S. Another mark there reads: Leipzig.
The model shows part of a surface that can be represented by the equation x2/a2 + y2/ b2 = - 2z (when the model is mounted on the stand as shown, the z-axis goes cross-wise). The stand is part of MA.304722.24.
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, p. 242.
M. Schilling, Catalog, 1911, p. 1-2, 114.
Currently not on view
Germany: Saxony, Leipzig
paper (overall material)
overall: 10 cm x 10 cm x 9.5 cm; 3 15/16 in x 3 15/16 in x 3 3/4 in
Gift of Brown University Department of Mathematics