Painting - Star Construction

Object Details

painter

Johnson, Crockett

Description

Crockett Johnson's interest in regular polygons included the pentagram, or five-pointed star. The relation between the pentagon and the star is simple. If each side of a regular pentagon is extended, a regular five-pointed star results. Similarly, connecting each diagonal of a regular pentagon creates a regular five-pointed star. The star will have a pentagon in it, so the method is self-perpetuating.

A method for a pentagram's construction in described in Book IV, Proposition II of Euclid's Elements, but the construction illustrated in this painting is the artist's own creation. It builds on the relationship between the sides of a regular five-pointed star and the golden ratio. As Crockett Johnson may have recalled from his earlier paintings, the five rectangles that surround the central pentagon of the star are golden, that is to say the ratio of the length of the two equal sides of the triangle to the side of the enclosed pentagon is (1 + √5) / 2. Hence one can construct the star by finding a line segment divided in this ratio. No figure by Crockett Johnson showing his construction has been found.

The pentagram, executed appropriately enough in hues of gold, contrasts vividly with the purple background in Star Construction.

The painting is #103 in the series. It is in oil or acrylic on pressed wood and has a gold-colored metal frame. The painting is unsigned and undated. Compare #46 (1979.1093.33) and #64 (1979.1093.39).

Location

Currently not on view

Credit Line

Ruth Krauss in memory of Crockett Johnson

1970-1975

ID Number

1979.1093.70

catalog number

1979.1093.70

accession number

1979.1093

Object Name

painting

Physical Description

masonite (substrate material)

metal (frame material)

Measurements

overall: 51.5 cm x 60.5 cm x 2.5 cm; 20 1/4 in x 23 13/16 in x in

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694694

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-2083-704b-e053-15f76fa0b4fa