Model of a Quartic Scroll by Richard P. Baker, Baker #84 (a Ruled Surface)
date: label: date made
content: ca 1915-1935
label: date made
content: ca 1905-1935
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 wooden base of this model reads: No. 84 Quartic Scroll, (/) with two nodal straight (/) lines. Model 84 appears on page 8 of Baker’s 1931 catalog of models as “<I>Quartic Scroll </I>, with two nodal straight lines.” The equation of the model is listed as (x<sup>2</sup>/((z - 1) <sup>2</sup>)) + (y<sup>2</sup>/((z + 1) <sup>2</sup>)) = 1. 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 is swept out by any of the yellow threads joining the elliptically shaped horizontal piece of wood on the top of the model to the wooden base of the model.
label: Description
content: In addition to the yellow threads of the model, there are two horizontal red threads that run from the rods at near the edge of the base and are parallel to the lines connecting the midpoints of the opposite sides of the square of surface of the base. There is a segment of each of these red threads for which each point meets two different lines of the model and the points of these segments are called double points, or nodes, of the surface. Thus these line segments are the two nodal lines of the model. The horizontal plane z = 1 intersects the model at the upper horizontal thread, while the horizontal plane z = -1 intersects it at the lower horizontal thread. When z=1, the points of intersection are (0,y,1) for y between -2 and 2. When z=-1, the points of intersection are (x,0,-1) for x between -2 and 2. Thus the nodal lines are the line segments connecting (0,-2,1) to (0,2,1) and (-2,0,-1) to (2,0,-1).
label: Description
content: When z = 0 the equation of the surface becomes x<sup>2</sup> + y<sup>2</sup> = 1, so the horizontal plane z = 0 intersects the model at the unit circle with center at the origin. For any other value of z, the equation of the surface is of the form (x<sup>2</sup>/a<sup>2</sup>) + (y<sup>2</sup>/b<sup>2</sup>) = 1, where a does not equal b. This is the standard form for the equation of an ellipse.
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.211257.010
label: accession number
content: 211257
label: catalog number
content: 211257.010
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: yellow (overall color)
label: Physical Description
content: black (overall color)
label: Physical Description
content: red (overall color)
label: Physical Description
content: bolted, threaded and tied (overall production method/technique)
label: Measurements
content: average spatial: 27.7 cm x 22.9 cm x 22.7 cm; 10 29/32 in x 9 1/32 in x 8 15/16 in