Model of the Polar Developable of a Twisted Cubic, by Richard P. Baker, Baker #146 ? (a Ruled Surface)

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.

The typed part of a paper label on the wooden base reads: “No. 146 (/) POLAR DEVELOPABLE (/) TW.CUBIC” and corresponds to one of four models in the museum collections that Baker listed in a section, “A Study of the Twisted Cubic,” of his 1931 catalog. The other three are MA.211257.023 (No. 139. Surface of binormals), MA.211257.024 (No. 140. Surface of tangents), and MA.211257.025 (No. 141. Rectifying developable). There is no wire curve surviving in model No. 140 (Surface of tangents). The curves in No. 139 (Surface of binormals) and No. 141 (Rectifying developable) are both twisted since neither of them lies in any plane in three space.

Unlike the wire curves in the Nos. 139 and 141, the wire curve shown in No. 146, Polar developable, appears to lie in a plane so may not be a twisted cubic as shown on its label. Another reason to believe that this model may have been mislabeled is that the polar developable of a twisted cubic would not consist of a set of parallel lines.

Reference:

Richard P. Baker, Mathematical Models, Iowa City, 1931, p. 12.

Currently not on view