Model of Translation by Two Reflections in a Line, by Richard P. Baker, Baker #116

This geometric model was constructed by Richard P. Baker in the early twentieth century when he was Associate Professor of 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.

This is one of several models Baker made that relate to projective geometry. More specifically, he wrote in the catalog of his models: “In Lie’s analysis of projective transformation occur eight elements. Illustrations of their composition, mostly intuitive, are:-.” Baker then listed the models to which he assigned numbers 115 through 128. This, apparently the only one of the set in the Smithsonian collections, is number 116, which Baker describes as “Translation by two reflexions in a line.”

The model is made of metal and includes three heavy wires with arrows on the ends. The longest arrow is painted blue on top and is not firmly attached to the model. The red and white arrows meet and are perpendicular to each other. They are also both are attached to a flat white metal piece that is roughly elliptical in shape. There is a blue metal surface in the shape of a cone through which the white surface passes. A mark in pencil reads: 116. This model does not have a typed paper label like others Baker used to indicate the title and number of the model.

Two loose pieces that may be associated with this model were noted by museum intern Kristin Haring in the 1990s. One consists of wires that closely resemble the arrows of the model except that the red arrow runs much closer to the blue section of the long arrow and there is a thinner wire with an ending that is shaped differently than an arrow. The second piece is the same as the thinner wire that was added to the wires of the model to form the first piece.

Because it is not clear what Baker’s model number 116 originally looked like, a full interpretation is not attempted. According to the accession file, a copy of model 116 (but no other models in the range 115 to 128) was sent by Baker’s descendants for exhibition at MIT in 1939 and later came to the Smithsonian.

References:

Richard P. Baker, Mathematical Models, Iowa City, 1931, pp. 14-15.

Accession file.

Currently not on view