Geometric Model, L. Brill No. 26. Carton Ser. No. 6, Hyperbolic Paraboloid Made from Cardstock
date: label: date made
content: 1892
name: label: maker
content: L. Brill
notes: label: Description
content: In the nineteenth and early twentieth century, students studying technical subjects often learned about the representation of surfaces by equations in courses in solid analytic geometry. Schools in Europe, the United States, and Japan sometimes purchased models to illustrate such surfaces. The firm of Ludwig Brill in Darmstadt published this one as part of a series of paper models (the “Carton” series) designed by Alexander Brill and first issued in 1874. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
label: Description
content: This tan paper model of a hyperbolic paraboloid consists of thirteen portions of triangles, intersecting portions of another thirteen triangles. It is stored flat in a gray envelope which in turn is in a brown paper box with the other models in the series. A mark stamped on the model reads: Verlag von L. Brill in Darmstadt.
label: Description
content: The saddle-shaped surface is represented by the equation: + y<sup>2</sup>/ b<sup>2</sup> - x<sup>2</sup>/a<sup>2</sup> = -2z. Sections by any plane where x = c or y=c (c being an arbitrary constant) are parabolas. Sections parallel to the plane z = 0 are hyperbolas. The top edges of the pieces are straight lines, illustrating that the hyperbolic paraboloid is a ruled surface.
label: Description
content: Compare MA.304723.669.
label: Description
content: References:
label: Description
content: Ludwig Brill, <I>Catalog mathematischer Modelle. . .</I>, Darmstadt: L. Brill, 1892, p. 1, 57.
label: Description
content: Henry Burchard Fine and Henry Dallas Thompson, <I>Coordinate Geometry</I>, New York: Macmillan Company, 1931, p. 243-244.
label: Location
content: Currently not on view
place: label: place made
content: Germany: Hesse, Darmstadt
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of Wesleyan University
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1985.0112.021
label: catalog number
content: 1985.0112.021
label: accession number
content: 1985.0112
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: paper (overall material)
label: Measurements
content: overall: 10 cm x 14 cm x 8 cm; 3 15/16 in x 5 1/2 in x 3 5/32 in