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L. Brill No. 163, Ser.13 No. 1, Ruled Surface with Two Real Double Lines and Four Pinch Points on Each of the Lines

Object Details

Description
The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 1 in the series.
The thread model has a metal frame. It shows two congruent ruled surfaces (in gold), as well as two double lines (in red). Each of the lines has four pinch points, that is to say points for which every neighborhood is self-intersecting.
The model was received at the Smithsonian with its threads broken and restrung.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 68.
“Mathematical Models of Surfaces”, University of Groningen, website accessed October 16, 2017. This site describes the mathematics of these surfaces in more detail. It illustrates them with examples of the models published by Brill’s successor, Martin Schilling.
Location
Currently not on view
Data Source
National Museum of American History
maker
L. Brill
date made
1892
Credit Line
Gift of Wesleyan University
Physical Description
string (overall material)
metal (overall material)
Measurements
overall: 18.5 cm x 25 cm x 12.2 cm; 7 9/32 in x 9 27/32 in x 4 13/16 in
Object Name
Geometric Model
geometric model
Geometric Model, L. Brill No. 163, Ser.13 No. 1, Ruled Surface with Two Real Double Lines and Four Pinch Points on Each of the Lines
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