Model of Culmann's Theorem by Richard P. Baker, Baker #432d
date: label: date made
content: ca 1906-1935
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: This geometric model was made by Richard P. Baker in the early twentieth century when he was on the faculty in mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over 100 of his models are in the museum collections.
label: Description
content: The object has a rectangular wooden base covered with paper on which lines of projection are marked. A wire structure in two parts extends above the base, indicating the line segments projected (at least one wire is missing). A paper tag reads: Culmann's Theorem (/) THE TWO FUNICULARS (/) With the two dual polyhedra orthogonally (/) projected to the force polygon and funicular. In his catalog, Baker writes: The two funiculars with the dual polyhedra whose orthogonal projections are the force polygon and funicular. Baker grouped this model with three others associated with Moebius’ theorem.
label: Description
content: Between 1864 and 1866, the German-born scholar Karl Culmann (1821-1881) of the Zurich Polytechnic Institute in Switzerland published a monograph on graphical statics from the point of view of projective geometry. He was particularly interested in connections between the funicular polygon (the figure assumed by a rope or cord with weights hanging from a number of points) and the force polygon (the diagram of the forces associated with the of the hanging weights).
label: Description
content: References:
label: Description
content: Baker, R. P., <I>Mathematical Models</I>, Iowa City, 1931, p. 13.
label: Description
content: Culmann, K. <I>Die graphische Statik</I>, Zurich: Meyer & Zeller,1866.
label: Description
content: Gerhardt, R., Kurrer, K., and Pichler, G., “The Methods of Graphical Statics and their Relation to the Structural Form,” <I>Proceedings of the First International Congress on Construction History</I>, Madrid, 20th-24th January 2003, ed. S. Huerta, Madrid: I. Juan de Herrera, SEdHC, ETSAM, A. E. Benvenuto, COAM, F. Dragados, 2003.
label: Location
content: Currently not on view
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 Frances E. Baker
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.211257.084
label: accession number
content: 211257
label: catalog number
content: 211257.084
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: wood (overall material)
label: Physical Description
content: metal (overall material)
label: Physical Description
content: red (overall color)
label: Physical Description
content: blue (overall color)
label: Physical Description
content: green (overall color)
label: Physical Description
content: black (overall color)
label: Physical Description
content: soldered.wire stuck in base. (overall production method/technique)
label: Measurements
content: average spatial: 15.9 cm x 28.4 cm x 34.6 cm; 6 1/4 in x 11 3/16 in x 13 5/8 in