Painting - Heptagon from Its Seven Sides

Object Details

painter

Johnson, Crockett

Description

Toward the end of his life, Crockett Johnson took up the problem of constructing a regular seven-sided polygon or heptagon. This construction, as Gauss had demonstrated, requires more than a straight edge and compass. Crockett Johnson used compass and a straight edge with a unit length marked on it. Archimedes and Newton had suggested that constructions of this sort could be used to trisect the angle and to find a cube with twice the volume of a given cube, and Crockett Johnson followed their example.

One may construct a heptagon given an angle of pi divided by seven. If an isosceles triangle with this vertex angle is inscribed in a circle, the base of the triangle will have the length of one side of a regular heptagon inscribed in that circle. According to Crockett Johnson's later account, in the fall of 1973, while having lunch in the city of Syracuse on Sicily during a tour of the Mediterranean, he toyed with seven toothpicks, arranging them in various patterns. Eventually he created an angle with his menu and wine list and arranged the seven toothpicks within the angle in crisscross patterns until his arrangement appeared as is shown in the painting.

Crockett Johnson realized that the vertex angle of the large isosceles triangle shown is exactly π/7 radians, as desired. The argument suggested by his diagram is more complex than what he later published. The numerical results shown in the figure suggest his willingness to carry out detailed calculations.

Heptagon from its Seven Sides, painted in 1973 and #107 in the series, shows a triangle with purple and white sections on a navy blue background. This oil or acrylic painting on masonite is signed on its back : HEPTAGON FROM (/) ITS SEVEN SIDES (/) (Color sketch for larger painting) (/) Crockett Johnson 1973. No larger painting on this pattern is at the Smithsonian.

Reference: Crockett Johnson, "A Construction for a Regular Heptagon," Mathematical Gazette, 1975, vol. 59, pp. 17–21.

Location

Currently not on view

Credit Line

Ruth Krauss in memory of Crockett Johnson

1973

ID Number

1979.1093.74

catalog number

1979.1093.74

accession number

1979.1093

Object Name

painting

Physical Description

masonite (substrate material)

aluminum (frame material)

Measurements

overall: 82 cm x 41.2 cm x 2.5 cm; 32 5/16 in x 16 1/4 in x in

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694698

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-1654-704b-e053-15f76fa0b4fa