Model of the Rectifiying Developable of a Twisted Cubic, by Richard P. Baker, Baker #141 (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. 141 (/) RECTIFYING DEVELOPABLE (/) TW.cubic THREAD. It is one of four models in the museum collections that Baker listed in a section, “A Study of the Twisted Cubic,” of his 1931 catalog (see MA.211257.023, MA.211257.024, and MA.211257.30). A twisted cubic is so called because it does not lie in any plane in three space and is often represented by the vector function of t: (t, t², t³). The notation Baker used in computing the surface known as the rectifying developable is the same as appears in a 1909 book, A Treatise on the Differential Geometry of Curves and Surfaces, by the American mathematician Luther Eisenhart. In this model the copper wire that runs between the two small pieces of wood fastened to the wooden base represents a twisted cubic.

The red threads represent a surface defined in terms of the binormals and tangents to the curve that is called the curve’s rectifying developable. Binormals and tangents to twisted cubics can be seen in MA.211257.023 and MA.211257.024, respectively.

Reference:

John B. Little, “The Many Lives of the Twisted Cubic,” The American Mathematical Monthly, 126 (2019) no. 7, pp. 579-592.

Currently not on view