Painting - Area and Perimeter 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 nineteenth century that the impossibility of squaring a circle was demonstrated.

This painting is an original construction by Crockett Johnson. It begins with the assumption that the circle has been squared, the area of the larger square equals that of the circle. Crockett Johnson then constructed a smaller square so that it has perimeter equal to the circumference of the circle. His diagram for the painting is shown, with the large square having side AB and the small one side of length AC.

The painting is #95 in the series. It has a black background. There is a rose circle superimposed on two gray squares. The painting is unsigned and has a metal frame.

Reference: Carl B. Boyer and Uta C. Merzbach, A History of Mathematics (1991), pp. 65-7, pp. 71–2.

Currently not on view