Geometric Model, L. Brill No. 141. Ser. 2 No. 8b, Surface of Revolution (Part of the Nodoid)
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 that had been 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. They 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 second in the group, shows part of a surface called a nodoid (the rest is model 1985.0112.101). The rounded figure looks something like a torus but the hole does not go all the way through. Various geodesics are indicated. A paper tag reads: 141. Another, torn tag reads: [. . .]sfl. const. mittl. Krümmg. (/) [. . .] L. Brill. 2. Ser. Nr. VIIIb.
label: Description
content: Fischer discusses the mathematics of these surfaces of constant mean curvature. D’Arcy W. Thompson describes the generation of such surfaces. In this case, suppose a fixed line asymptotic to one branch of a hyperbola rolls until the line is asymptotic to the other branch. The second branch then rolls with respect to the line. The motion of the foci of the hyperbola then generates a succession of kinks which, when revolved by the meridianal line about the axis, generate the two sections of the nonoid (1985.0112.100 and 1985.0112.101).
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
label: See more items in
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: 1985.0112.100
label: catalog number
content: 1985.0112.100
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: 7.5 cm x 12 cm x 12 cm; 2 15/16 in x 4 23/32 in x 4 23/32 in