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


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.


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.

Date Made: 1892

Maker: L. Brill

Location: Currently not on view

Place Made: Germany: Hesse, Darmstadt

Subject: Mathematics


See more items in: Medicine and Science: Mathematics, Science & Mathematics


Exhibition Location:

Credit Line: Gift of Wesleyan University

Data Source: National Museum of American History

Id Number: 1985.0112.134Catalog Number: 1985.0112.134Accession Number: 1985.0112

Object Name: Geometric Modelgeometric model

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

Guid: http://n2t.net/ark:/65665/ng49ca746a5-1ca8-704b-e053-15f76fa0b4fa

Record Id: nmah_694010

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