Painting - Euclidian Values of a Squared Circle

To "square" a figure, according to the classical Greek tradition, means to construct, with the aid of only straightedge and compass, a square equal in area to that of the figure. The Greeks could square numerous figures, but were unsuccessful in efforts to square a circle. It was not until the 19th century that the impossibility of squaring a circle was demonstrated.
This painting is an original construction by Crockett Johnson. It begins with the assumprion that the circle has been squared. In this case, Crockett Johnson performed a sequence of constructions that produce several additional squares, rectangles, and circles whose areas are geometrically related to that of the original circle. These figures are produced using traditional Euclidean geometry, and require only straightedge and compass.
The painting on masonite is #102 in the series. It has a blue-black background and a metal frame. It shows various superimposed sections of circles, squares, and rectangles in shades of light blue, dark blue, purple, white and blue-black. It is unsigned. See 1979.3083.02.13.
References: Carl B. Boyer and Uta C. Merzbach, A History of Mathematics (1991), Chapter 5.
Crockett Johnson, "A Geometrical Look at the Square Root of Pi," Mathematical Gazette 54 (February, 1970): pp. 59–60.
Currently not on view
Object Name
date made
ca 1970
Johnson, Crockett
Physical Description
masonite (substrate material)
metal (frame material)
overall: 122.5 cm x 82 cm x 2.5 cm; 48 1/4 in x 32 5/16 in x 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


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