Model of Surface of Binormals to a Twisted Cubic by Richard P. Baker, Baker #139 (a Ruled Surface)

Model of Surface of Binormals to a Twisted Cubic by Richard P. Baker, Baker #139 (a Ruled Surface)

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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.
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 MA.211257.024, MA.211257.025, 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 of binormals 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 from one side of the wooden base to the opposite side represents a twisted cubic.
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.
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
Object Name
geometric model
date made
ca 1906-1935
Associated Date
ca. 1905-1931
Baker, Richard P.
Physical Description
thread (overall material)
wood (overall material)
metal (overall material)
yellow (overall color)
copper (overall color)
black (overall color)
screwed and threaded (overall production method/technique)
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
ID Number
accession number
catalog number
Credit Line
Gift of Frances E. Baker
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Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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