Painting - Squares of 2, 4, 16 from Square Root of x

In this painting, Crockett Johnson supposed that one was given two lengths, one the square root of the second. Although no numerical values were given, he sought to construct three squares, one the square root of the second and the second the square root of the third, and to give their values numerically. His solution is represented in the painting, and described in his notes as work from 1972.
The three squares are visible, one the entire surface of the painting and the two others within it. The vertical lines point to the starting point of the painting, a line segment along the base and its square root. From here, Crockett Johnson constructed the elaborate geometrical argument illustrated by the painting. He claimed that he had constructed squares of area 2, 4, and 16. The ratios of the areas are as he describes, but the absolute numerical values depend on the units of measure.
This oil painting on masonite is #88 in the series. It is unsigned. There is an inset metal strip in the wooden frame.
Currently not on view
Object Name
date made
Johnson, Crockett
Physical Description
masonite (substrate material)
wood (frame material)
metal (frame material)
overall: 122 cm x 120.6 cm x 3.8 cm; 48 1/16 in x 47 1/2 in x 1 1/2 in
ID Number
catalog number
accession number
Science & Mathematics
Crockett Johnson
See more items in
Medicine and Science: Mathematics
Crockett Johnson
Data Source
National Museum of American History, Kenneth E. Behring Center
Credit Line
Ruth Krauss in memory of Crockett Johnson
Additional Media

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