Model of a Cubic Cone with Nodal Line by Richard P. Baker, Baker #78 (a Ruled Surface)

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.
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 Cubic Cones . It also appears in his 1905 catalog of one hundred models.
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.
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=x3, it would be at the origin). This line is horizontal and passes over the center of the base.
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.
Currently not on view
date made
ca 1900-1935
Baker, Richard P.
place made
United States: Iowa, Iowa City
Physical Description
thread (overall material)
wood (overall material)
metal (overall material)
red (overall color)
black (overall color)
screwed and threaded (overall production method/technique)
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
ID Number
accession number
catalog number
Credit Line
Gift of Frances E. Baker
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Mathematical Association of America Objects
Data Source
National Museum of American History, Kenneth E. Behring Center


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