Model for the Petersen-Morley Theorem by Richard P. Baker, Baker #441

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.

Now in stored in a cardboard box with lid, the painted wire structure is presently in four pieces.

This is one of nine models Baker built to correspond to figures described by the German mathematician Eduard Study inthe book cited below (Baker shortened the title to Dynamen). Baker described it in his 1931 catalog as representing the “Petersen-Morley theorem.”

The Petersen-Morley theorem was developed independently by the Danish mathematician Johannes Petersen (1873-1950) and the English-born American mathematician Frank Morley (1860-1937). {Johannes Petersen would change his last name to Hjelmslev}. The theorem relates to the properties of line segments of shortest distance joining three skew lines. Morley presented a model relating to the theorem to the London Mathematical Society in 1898 and, after he had moved to the United States, an expanded version of it to the American Mathematical Society in 1899. Study also cites Petersen’s work from 1898.

References:

Baker, R.P., Mathematical Models, Iowa City, 1931, p. 16.

Lützen, J. "The Mystery of Ten Wooden Blocks: Hjelmslev’s Geometry of Reality," Math Semesterber,2020, vol. 67, pp. 161-167.

Study, E., Geometrie der Dynamen: Die Zusammensetzung von Kräften und Verwandte Gegenstände der Geometrie Bearb., Leipzig: B.G. Teubner, 1903, esp. pp. 106-107.

Currently not on view