Painting - Pi Squared and Its Square Root

This painting is part of Crockett Johnson's exploration of constructions that might take place if one could draw squares equal in area to circles. It incorporates elements of a figure in his papers that includes two squares and a rectangle. The smaller square (ABDX in Crockett Johnson's figure) is defined as having the same area as a circle, CFXE,circumscribing the rectangle (the rectangle of sides CE and EX in the figure).
The circle is assumed to have radius one. Hence the area of the square is supposed to be pi, and the length of its side (e.g. AB or CF) the square root of pi. The area of the rectangle is assumed to be the square root of pi. Hence one has a painting that includes a square of area equal to pi and a rectangle of area equal to its square root. From such assumptions, Crockett Johnson went on to construct a line segment of length pi, which is not shown in the painting but does appear in the figure.
The painting is #83 in the series. It is in oil or acrylic on masonite. There is a black wooden frame. The work is unsigned and undated.
Currently not on view
Object Name
date made
Johnson, Crockett
Physical Description
masonite (substrate material)
wood (frame material)
overall: 70 cm x 84.4 cm x 3.8 cm; 27 9/16 in x 33 1/4 in x 1 1/2 in
ID Number
catalog number
accession number
See more items in
Medicine and Science: Mathematics
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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