Painting - Every Positive Integer (Gauss)

Object Details

referenced

Gauss, Carl Friedrich

painter

Johnson, Crockett

Description

This painting is loosely based on a theorem proven by the German mathematician Carl Friedrich Gauss (1777–1855) in 1776 when he was just nineteen years old. The proposition, one of Gauss’s many contributions to the branch of mathematics called number theory, states that every positive integer is the sum of three triangular numbers. The concept of triangular numbers dates to antiquity. Suppose one arranges dots in rows, with one in the first row, two in the second, three in the first and so forth. Three dots form a triangle, as do 6 dots, 10 dots, and 15 dots. The numbers 3, 6, 10, 15, and so forth are called "triangular numbers." The integers 0 and 1 are thought of as special cases of triangular numbers.

Crockett Johnson derived his painting from an entry in Gauss's diary published in an article by Eric Temple Bell included by James R. Newman in his book The World of Mathematics (1956), p. 304. The entry includes the phrase EUREKA in Greek, and indicates that any positive integer is the sum of three triangular numbers.

Crockett Johnson’s painting abstractly represents this theorem through the juxtaposition of three triangles. The triangles are equal, but each figure is painted a different color. It is possible that the artist chose to illustrate each triangle in its own color to demonstrate that each triangle generally represents its own triangular number when computing a positive integer. However, the triangles are congruent, which reminds the viewer that the triangles are related because they all represent a triangular number.

This work was painted in oil on masonite, completed in 1966, and is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) EVERY POSITIVE INTEGER (/) (GAUSS). It is painting #29 in the series, and has a wooden frame.

Reference: J. R. Newman, The World of Mathematics, 1956, p. 304.

Location

Currently not on view

Credit Line

Ruth Krauss in memory of Crockett Johnson

1966

ID Number

1979.1093.21

catalog number

1979.1093.21

accession number

1979.1093

Object Name

painting

Physical Description

masonite (substrate material)

wood (frame material)

Measurements

overall: 25.5 cm x 83 cm x 3.8 cm; 10 1/16 in x 32 11/16 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_694645

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-17fb-704b-e053-15f76fa0b4fa