# Painting - Pi Squared and Its Square Root

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 is based on a figure that includes two squares and a rectangle. The smaller square (ABDX in Crockett Johnson's figure) is defined as having the same area as the circle circle with center O and diameters the diagonals of the rectangle with sides CE and EX. This circle also appears in his other diagram, although it does not appear in the painting. Other assumptions concerning the upper diagram are that the rectangle has area the square root of the area of the circle and that the triangles with sides CX and PX are isosceles and congruent.
If the small circle has radius one.and the are of the rectangle is assumed to be the square root of the area of that circle and the small square, the area of the rectangle is the square root of pi.
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
1970-1975
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