Painting -Seventeen Sides (Gauss)

Object Details

referenced

Gauss, Carl Friedrich

painter

Johnson, Crockett

Description

Those making mathematical instruments for surveying, navigation, or the classroom have long been interested in creating equal divisions of the circle. Ancient geometers knew how to divide a circle into 2, 3, or 5 parts, and as well as into multiples of these numbers. For them to draw polygons with other numbers of sides required more than a straightedge and compass.

In 1796, as an undergraduate at the University of Göttingen, Friedrich Gauss proposed a theorem severely limiting the number of regular polygons that could be constructed using ruler and compass alone. He also found a way of constructing the 17-gon.

Crockett Johnson, who himself would develop a great interest in constructing regular polygons, drew this painting to illustrate Gauss's discovery. His painting follows a somewhat later solution to the problem presented by Karl von Staudt in 1842, modified by Heinrich Schroeter in 1872, and then published by the eminent mathematician Felix Klein. Klein's detailed account was in Crockett Johnson's library, and a figure from it is heavily annotated.

This oil painting on masonite is #70 in the series. It is signed: CJ69. The back is marked: SEVENTEEN SIDES (GAUSS) (/) Crockett Johnson 1969. The painting has a black background and a wood and metal frame. There are two adjacent purple triangles in the center, with a white circle inscribed in them. The triangles have various dark gray regions, and the circle has various light gray regions and one dark gray segment. The length of the top edge of this segment is the chord of the circle corresponding to length of the side of an inscribed 17-sided regular polygon.

Reference: Felix Klein, Famous Problems of Elementary Geometry (1956), pp. 16–41, esp. 41.

Location

Currently not on view

Credit Line

Ruth Krauss in memory of Crockett Johnson

1969

ID Number

1979.1093.45

accession number

1979.1093

catalog number

1979.1093.45

Object Name

painting

Physical Description

masonite (substrate material)

wood (frame material)

metal (frame material)

Measurements

overall: 124 cm x 63.5 cm x 3.8 cm; 48 13/16 in x 25 in x 1 1/2 in

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694669

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-28b5-704b-e053-15f76fa0b4fa