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Painting - Heptagon Stated By Seven Toothpicks (Between Parallels)

Painting - Heptagon Stated By Seven Toothpicks (Between Parallels)

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This whimsical painting is part of Crockett Johnson's exploration of ways to represent the sides and angles of a regular heptagon using line segments of equal length. In its mathematics, it follows closely the construction from isosceles triangles within a rhombus used in the painting Heptagon from Ten Equal Lines (#104 in the series - 1979.1093.71). However, both the line segments shown and the appearance of the paintings are quite different.
Here three pairs of carefully selected equal lines at appropriate equal angles combine with a seventh line of equal length to give a construction of three sides and two angles of a regular heptagon. All but one of the endpoints of the lines lie on a parallelogram (the rhombus mentioned previously), hence the title. The segment of the heptagon is on the right side of the painting. In Crockett Johnson's figure for the work, the segment is lettered BCPE.
The painting, in oil or acrylic on masonite, is #106 in the series. It has a dark purple background. The pairs of line segments are in turquoise, green, and lavender, with the vertical one in white. This increases the drama of the painting, but obscures the heptagon. There is a wooden frame. The painting is signed on the back: HEPTAGON STATED BY (/) SEVEN TOOTHPICKS (/) (BETWEEN PARALLELS) (/) Crockett Johnson 1973.
Currently not on view
Object Name
date made
Johnson, Crockett
Physical Description
masonite (substrate material)
metal (frame material)
overall: 67 cm x 41.5 cm x 2.9 cm; 26 3/8 in x 16 5/16 in x 1 1/8 in
ID Number
catalog number
accession number
Credit Line
Ruth Krauss in memory of Crockett Johnson
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Crockett Johnson
Data Source
National Museum of American History
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