Model of a Cubic Cone with Nodal Line by Richard P. Baker, Baker #78 (a Ruled Surface)
date: label: date made
content: ca 1900-1935
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: 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.
label: Description
content: The typed part of a paper label on the bottom of the wooden base of this model reads: No. 78 (/) CUBIC CONE WITH NODAL LINE. Model 78 appears on page 7 of Baker’s 1931 catalog of models as “With nodal line” under the heading <I>Cubic Cones </I>. It also appears in his 1905 catalog of one hundred models.
label: Description
content: Baker’s string models always represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows two ruled surfaces. One of these surfaces is swept out by any of the threads connecting the curved vertical wooden sides of the model. The other ruled surface is swept out by any of the threads joining the curved horizontal piece of wood on the top of the model to the wooden base of the model. All the threads of this model pass through a point in the center of the model, which is the intersection of two special lines, one for each ruled surface.
label: Description
content: The special line for the surface joining the vertical sides is the line connecting the inflection points of the cubic curves, i.e. the points where the curve changes from concave upward to concave downward (for the curve y=x<sup>3</sup>, it would be at the origin). This line is horizontal and passes over the center of the base.
label: Description
content: The special line for the other curve is the vertical line going through the center of the base. It is formed by connecting the point where the upper curve crosses itself with the center of the base, which is also the point where the curve on the base crosses itself. A point of curve where the curve crosses itself is called a node, so all points of this vertical line are nodes and this is the nodal line of the surface.
label: Location
content: Currently not on view
place: label: place made
content: United States: Iowa, Iowa City
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Mathematical Association of America Objects
publisher: label: Related Publication
content: Baker, Richard P.. Mathematical Models
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.211257.006
label: accession number
content: 211257
label: catalog number
content: 211257.006
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: red (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: 20.2 cm x 17.7 cm x 17.8 cm; 7 15/16 in x 6 31/32 in x 7 in