Model of Culmann's Theorem by Richard P. Baker, Baker #432d

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.

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.

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).

References:

Baker, R. P., Mathematical Models, Iowa City, 1931, p. 13.

Culmann, K. Die graphische Statik, Zurich: Meyer & Zeller,1866.

Gerhardt, R., Kurrer, K., and Pichler, G., “The Methods of Graphical Statics and their Relation to the Structural Form,” Proceedings of the First International Congress on Construction History, Madrid, 20th-24th January 2003, ed. S. Huerta, Madrid: I. Juan de Herrera, SEdHC, ETSAM, A. E. Benvenuto, COAM, F. Dragados, 2003.

Currently not on view