Geometric Models, L. Brill No. 99. Ser. 3 No. 9, Two Hyperboloids of Two Sheets

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. These objects are part of series of models of quadric surfaces (surfaces of degree two) designed in 1878 by Rudolf Diesel, then a student at the technical high school in Munich. They were published by the firm of Ludwig Brill in Darmstadt. These examples were exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where they were purchased by Wesleyan University.

The plaster models show a hyperboloid of two sheets. The surface can be represented by the equation x2/a2 + y2/ b2 + z2/c2 = - 1. Sections parallel to the plane z=0 are ellipses. Sections by the planes x=0 and y=0, and planes parallel to these, are hyperbolas. Two metal rods hold together the two sheets of each model.

Grids of perpendicular lines of curvature are shown. A paper tag on one models reads: 99. Paper tags on both of them read: Zweischaliges Hyperboloid. (/) Verl. v. L. Brill. 3. Ser. Nr. 9.

Compare 1990.0571.07.

References:

Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 7, 77.

Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 240-241.

Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 62, vol. II, pp.25-28.

Date Made: 1892

Maker: L. Brill

Location: Currently not on view

Place Made: Germany: Hesse, Darmstadt

Subject: Mathematics

Subject:

See more items in: Medicine and Science: Mathematics, Science & Mathematics

Exhibition:

Exhibition Location:

Credit Line: Gift of Wesleyan University

Data Source: National Museum of American History

Id Number: 1985.0112.072Catalog Number: 1985.0112.072Accession Number: 1985.0112

Object Name: Geometric Modelgeometric model

Physical Description: metal (overall material)plaster (overall material)Measurements: each: 23.5 cm x 21 cm x 13 cm; 9 1/4 in x 8 9/32 in x 5 1/8 in

Guid: http://n2t.net/ark:/65665/ng49ca746a5-2924-704b-e053-15f76fa0b4fa

Record Id: nmah_693948

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.