Paper Model of a Hyperbolic Paraboloid, M. Schilling No. 35, Carton Ser. No. 6
date: label: date made
content: ca 1903
label: date made
content: ca 1900
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 and its successor Martin Schilling in Leipzig 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 published by Schilling.
label: Description
content: This tan paper model of a hyperbolic paraboloid consists of thirteen portions of triangles, intersecting potions of another thirteen triangles. It is stored flat in a light green envelope which in turn is in a brown paper box with the other models in the series. A tag on the model reads: Karton-Modelle (/) von Flachen zweiter Ordnung. (/) Nr. 6. (/) Hyperbolisches Paraboloid. (/) Verlag von Martin Schilling in Halle a. S. A further mark on the envelope reads: Leipzig.
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.304723.19 to 1985.0112.021.
label: Description
content: References:
label: Description
content: Ludwig Brill, <I>Catalog mathematischer Modelle. . .</I>, Darmstadt: L. Brill, 1892, p. 1, 57.
label: Description
content: M. Schilling, <I>Catalog mathematischer Modelle. . .</I>, Leipzig, 1911, p.1-2, 114.
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: Saxony, Leipzig
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 Brown University Department of Mathematics
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.304722.19
label: catalog number
content: 304722.19
label: accession number
content: 304722
objectType: label: Object Name
content: Geometric Model
label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: paper (overall material)
label: Measurements
content: overall: 9.7 cm x 16.5 cm x 6.5 cm; 3 13/16 in x 6 1/2 in x 2 9/16 in