Model of a Cubic Surface by Richard P. Baker, Baker #430
date: label: date made
content: ca 1906-1935
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 one hundred of his models are in the museum collections.
label: Description
content: A typed label attached to a side of this model reads No. 430 (/) CUBIC SURFACE xyz-y+z=0. An entry for this model is in Baker's 1931 catalog in the section on "Analytic Geometry (/) Cyclides." Cyclides are quartic, not cubic, surfaces (e.g. they are of degree 2, not degree 3), which makes this grouping puzzling.
label: Description
content: Although the model appears to be divided into four regions, the cubic surface has three separate components. In the photographs NMAH-DOR2014-00228 and NMAH-DOR2014-00230 one can see that one of the three components is colored pink and appears to have all z values positive and that another which is diagonally opposite it appears to have all z values negative. As seen in the same photographs, the third component is comprised of the part of the surface that is colored yellow and the part of the surface that appears above the label.
label: Description
content: We can determine which is the first octant, i.e., where all three coordinates are either 0 or are positive, by looking at the vertical diagonals, y= x and y=-x. By substituting y for -x in the original equation we find that vertical diagonal is not defined for x=1 and x=-1. As can be seen on the two photographs listed above, this implies that y=-x is the vertical diagonal that intersects the two small components and, therefore, that the portion of the surface for which x=y must be contained in the union of the first octant and the octant in which all the coordinates are either 0 or are negative.
label: Description
content: On that vertical diagonal the equation of the surface becomes x<sup>2</sup>z – x + z=0 so z=x/(x<sup>2</sup> + 1). Since the denominator is always positive, z and x must have the same sign along the diagonal. It is clear from the first photograph listed above that the octant above the label satisfies the condition needed to be the first octant.
label: Description
content: An entry describing this model appears in Baker’s 1931 catalog in an untitled subsection of the section on Analytic Geometry that follows the Cyclides subsection.
label: Description
content: Reference:
label: Description
content: Richard P. Baker, Mathematical Models, Iowa City, 1931, p. 10.
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.211257.080
label: accession number
content: 211257
label: catalog number
content: 211257.080
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: plaster (overall material)
label: Physical Description
content: wood (overall material)
label: Physical Description
content: metal (overall material)
label: Physical Description
content: pink (overall color)
label: Physical Description
content: green (overall color)
label: Physical Description
content: yellow (overall color)
label: Physical Description
content: blue (overall color)
label: Physical Description
content: plaster cast, bolted to base. (overall production method/technique)
label: Measurements
content: average spatial: 12 cm x 19.7 cm x 20.1 cm; 4 23/32 in x 7 3/4 in x 7 29/32 in