Model of a Twisted Cubic by Richard P. Baker, Baker #74 (a Ruled Surface)

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Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 74 (/) TWISTED CUBIC: 3 real (/) asymptotes.
Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of three hyperbolic cylinders, one with yellow strings, one with blue strings, and one with red strings (a hyperbolic cylinder is a surface that joins two parallel hyperbolas, just as a regular cylinder joins two parallel circles. For a model, see 1982.0795.33). The hyperbolic cylinders in this model all make an acute angle with the base. Three pieces of wire indicate places where the three hyperbolic cylinders intersect. These are part of a curve of degree three known as a twisted cubic, in this case a twisted cubic with three real asymptotes.
The model sold for $7.50.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72. R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
Physical Description
thread (overall material)
wood (overall material)
metal (overall material)
red (overall color)
blue (overall color)
yellow (overall color)
black (overall color)
screwed and threaded (overall production method/technique)
Measurements
average spatial: 28 cm x 26.2 cm x 25.1 cm; 11 1/32 in x 10 5/16 in x 9 7/8 in
ID Number
MA.211257.003
accession number
211257
catalog number
211257.003
Credit Line
Gift of Frances E. Baker
subject
Mathematics
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History