Geometric Model, L. Brill No. 126. Ser. 5 No. 13b, Surface of Rotation

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In an 1862 paper on the deformation of surfaces, Edmond Bour (1832-1866), a French mining engineer who went on to serve as a lecturer in descriptive geometry and then professor of mechanics at the École polytechnique in Paris, included drawings of surfaces of revolution of constant positive curvature. These inspired Peter Vogel (1856-1915), an assistant in Munich, to design a set of three models that were first published by Brill in 1878 as part of Brill's Series V. This is one of these models, a second one is 1985.0112.091. This example was exhibited at the Columbia Exposition held in Chicago in 1893 and then acquired by Wesleyan University.
The white plaster model is round at the center and pointed at both ends. The curves shown on the surface are geodesics.
Edmond Bour, “Mémoire sur la déformation des surfaces,” Journale de l’École Polytechnique, 22, 39e cahier, 1862, pp. 35-84. For information about Bour, see the MacTutor website.
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 11, 80. Brill described the surface as of "spindle type."
G. Fischer, Mathematical Models: Commentary, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 32-33. Helmut Reckziegel, writing in Fischer’s volume, calls this a spindle-shaped form of a surface of revolution of constant curvature.
Ulf Hashagen, “ Die Mathematik und ihre Assistenten an der TH Munchen (1868-1918), Mathematics and Theoretical Physics, Symposia Gaussiana, ed. M. Behara, R. Fritsch, and R.G. Lintz, 1995, pp. 136-140.
Currently not on view
date made
L. Brill
place made
Deutschland: Hessen, Darmstadt
Physical Description
plaster (overall material)
overall: 7 cm x 7 cm x 11 cm; 2 3/4 in x 2 3/4 in x 4 11/32 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
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Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History