Geometric Model, L. Brill No. 26. Carton Ser. No. 6, Hyperbolic Paraboloid Made from Cardstock

Object Details

L. Brill

Description

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.

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.

The saddle-shaped surface is represented by the equation: + y²/ b² - x²/a² = -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.

Compare MA.304723.669.

References:

Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 1, 57.

Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, p. 243-244.

Location

Currently not on view

Credit Line

Gift of Wesleyan University

1892

ID Number

1985.0112.021

catalog number

1985.0112.021

accession number

1985.0112

Object Name

geometric model

Physical Description

paper (overall material)

Measurements

overall: 10 cm x 14 cm x 8 cm; 3 15/16 in x 5 1/2 in x 3 5/32 in

place made

Germany: Hesse, Darmstadt

See more items in

Medicine and Science: Mathematics

Science & Mathematics

National Museum of American History

Subject

Mathematics

Record ID

nmah_693897

Metadata Usage (text)

CC0

GUID (Link to Original Record)

https://n2t.net/ark:/65665/ng49ca746a5-228a-704b-e053-15f76fa0b4fa