Geometric Model by Richard P. Baker, Axial Pencil and Transversals, Baker #235

This geometric model was constructed by Richard P. Baker when he was Associate Professor of Mathematics at the University of Iowa, most likely some time before 1930. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label taped to this wire model reads: No. 235 (/) Axial pencil (/) transversals. Model 235 appears on page 13 of Baker’s 1931 catalog of models as “Axial Pencil and transversals.”

An axial pencil is a set of planes that pass through a line, called the axis of the pencil. The most obvious of the axial pencils represented in the model has its axis as the short rod parallel to the long rods of the base of the model. Each long rod of the base produces a plane that goes through the axis. One of the planes includes the yellow rods, the other the pink rods.

The transversals in the title probably refer to the short rods connecting the long rods of the base. These short rods will be referred to as base transversals. There are two more rods parallel to these transversals, one at the top of the model and one, much shorter, slightly above the axis of the pencil described above, each of which is the axis of another axial pencil represented in the model. The colors of some of the rods are no longer very clear. However, it appears as if the original coloring would have been useful in describing these two additional axial pencils.

Each base transversal meets two vertical rods and produces a plane that goes through one of the other two transversals. The triangles formed by each of the center three base transversals meet the upper non-base transversal. Thus the plane of each of those three triangles is a part of the axial pencil with axis the transversal at the top of the model. The triangles formed by each of the outer two base transversals meet the very short non-base transversal. Thus the plane of each of those triangles is part of the axial pencil with axis the very short transversal.

Currently not on view