Model of the Rectifiying Developable of a Twisted Cubic, by Richard P. Baker, Baker #141 (a Ruled Surface)

Object Details

Baker, Richard P.

Description

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.

Location

Currently not on view

Credit Line

Gift of Frances E. Baker

ca 1906-1935

ID Number

MA.211257.025

accession number

211257

catalog number

211257.025

Object Name

geometric model

Physical Description

thread (overall material)

wood (overall material)

metal (overall material)

black (overall color)

copper (overall color)

red (overall color)

screwed and threaded. (overall production method/technique)

Measurements

average spatial: 20.6 cm x 25.7 cm x 25.7 cm; 8 1/8 in x 10 1/8 in x 10 1/8 in

See more items in

Medicine and Science: Mathematics

Science & Mathematics

National Museum of American History

Subject

Mathematics

Record ID

nmah_1081141

Metadata Usage (text)

CC0

GUID (Link to Original Record)

https://n2t.net/ark:/65665/ng49ca746a9-3018-704b-e053-15f76fa0b4fa