Model of Surface of Binormals to a Twisted Cubic by Richard P. Baker, Baker #139 (a Ruled Surface)
date: label: date made
content: ca 1906-1935
label: Associated Date
content: ca. 1905-1931
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: 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.
label: Description
content: A typed paper tag glued to the base of the model reads: No. 139 (/) SURFACE OF BINORMALS TO (/) TW. CUBIC THREAD. This 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 also MA.211257.024, MA.211257.025, and MA.211257.30).
label: Description
content: 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, t<sup>2</sup>, t<sup>3</sup>). The notation Baker used in computing the surface of binormals is the same as appears in a 1909 book, <I>A Treatise on the Differential Geometry of Curves and Surfaces</I>, by the American mathematician Luther Eisenhart. In this model the copper wire that runs from one side of the wooden base to the opposite side represents a twisted cubic.
label: Description
content: The binormals to this curve are represented by the yellow threads, which means that the threads meet the curve where they are perpendicular to the osculating plane. The term osculating derives from the Latin for kissing and in three-dimensional geometry mathematicians use the term to refer to the plane formed by the tangent and normal vectors at the point.
label: Description
content: Reference:
label: Description
content: John B. Little, “The Many Lives of the Twisted Cubic,” <I>The American Mathematical Monthly</I>, 126 (2019) no. 7, pp. 579-592.
label: Location
content: Currently not on view
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
label: See more items in
content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of Frances E. Baker
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.211257.023
label: accession number
content: 211257
label: catalog number
content: 211257.023
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: thread (overall material)
label: Physical Description
content: wood (overall material)
label: Physical Description
content: metal (overall material)
label: Physical Description
content: yellow (overall color)
label: Physical Description
content: copper (overall color)
label: Physical Description
content: black (overall color)
label: Physical Description
content: screwed and threaded (overall production method/technique)
label: Measurements
content: average spatial: 27.9 cm x 25.2 cm x 25.6 cm; 10 31/32 in x 9 29/32 in x 10 3/32 in