Painting  Pi Squared and Its Square Root
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 Description

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.
 Location

Currently not on view
 date made

19701975
 painter

Johnson, Crockett
 Physical Description

masonite (substrate material)

wood (frame material)
 Measurements

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

overall: 29 in x 2 in x 35 in; 73.66 cm x 5.08 cm x 88.9 cm
 ID Number

1979.1093.54
 catalog number

1979.1093.54
 accession number

1979.1093
 Credit Line

Ruth Krauss in memory of Crockett Johnson
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Medicine and Science: Mathematics

Science & Mathematics

Art

Crockett Johnson
 Data Source

National Museum of American History