Geometric Model, L. Brill No. 143. Ser. 2 No. 8d, Surface of revolution, Catenoid
date: label: date made
content: 1892
name: label: maker
content: L. Brill
notes: label: Description
content: In 1877, Ludwig Brill published three models of surfaces of revolution of constant mean curvature (one in two parts). They were designed by A. von Braunmühl (1853-1908), a student and later teacher of mathematics in Munich who would become a well-known historian of mathematics. These were among the first plaster models Brill published, and were casts after models in the technical institute in Munich where Braunmühl studied, carried out under the direction of Alexander Brill.
label: Description
content: This model, the last in the group, shows a catenoid, that is to say a surface of revolution of a catenary. It has a round, flat bottom and a smaller round, flat top with an indentation in between. Various geodesics are indicated in red, green, and white.
label: Description
content: Fischer discusses the mathematics of these surfaces of constant mean curvature. D’Arcy W. Thompson describes the generation of such surfaces. If a parabola rolls along a straight line, its focus moves in a catenary. Rotating this catenary about the straight line gives the catenoid of the model.
label: Description
content: References:
label: Description
content: L. Brill, <I>Catalog mathematischer Modelle. . .</I>, Darmstadt: L. Brill,1892, p. 5, 83. This catalog indicates there were four models in series. The two parts of the nodoid are listed separately.
label: Description
content: [Advertisement], “Models Manufactured by L. Brill in Darmstadt,” <I>American Journal of Mathematics</I>, vol. XI, no. 3, April, 1889, end pages.
label: Description
content: G. Fischer, <I>Mathematical Models: Commentary</I>, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 47-48.
label: Description
content: Mathematics Institute of Oxford University website.
label: Description
content: D’Arcy Wentworth Thompson, <I>On Growth and Form</I>, I, Cambridge: University Press, 1963, pp. 367-369.
label: Location
content: Currently not on view
place: label: place made
content: Germany: Hesse, Darmstadt
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of Wesleyan University
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1985.0112.102
label: catalog number
content: 1985.0112.102
label: accession number
content: 1985.0112
objectType: label: Object Name
content: Geometric Model
label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: plaster (overall material)
label: Measurements
content: overall: 10 cm x 16.5 cm x 16.5 cm; 3 15/16 in x 6 1/2 in x 6 1/2 in