# Painting -Approximation of Pi to .0001

Description
In this painting, Crockett Johnson continued his exploration of ways to find rectilinear figures of area approximately equal to pi with another of his own constructions. He took advantage of the fact that the square root of two is 1.414214, while pi is approximately 3.141597. By constructing a length of one tenth the √2 and adding it to length three, he had a length 3.1414214 which, in his language, is an approximation of pi to .0001.
Here he assumed that the two large overlapping circles both have diameter two, and the smaller circle diameter one. The three blue and white squares then have sides of length one and diagonals of length √2. Suppose (as Crockett Johnson does) that one marks off a length of 1/10 along the side of the rightmost square, and erects a perpendicular. It will cut the diagonal of the small square to form a right triangle that has hypotenuse of length equal to one tenth √2, as desired. This then serves as the radius of a small circular arc, and is added on to the length of the sides of the three unit squares to form an approximate value of pi.
A diagram from Crockett Johnson's papers presents the mathematics of his construction.
The painting is #101 in the series. It has a black border and is unframed. It shows two overlapping circles of the same size, a smaller of half the diameter, and the arc of a still smaller circle. The circles are divided by straight lines into turquoise and white sections on the bottom, which form the area approximately equal in area to one of the large circles. The length approximately equal to pi is across the bottom. Sections at the top are in dark purple and black.
Location
Currently not on view
1970-1975
painter
Johnson, Crockett
Physical Description
masonite (substrate material)
Measurements
overall: 61 cm x 82 cm x .6 cm; 24 in x 32 5/16 in x 1/4 in
overall: 25 in x 2 in x 34 in; 63.5 cm x 5.08 cm x 86.36 cm
ID Number
1979.1093.68
catalog number
1979.1093.68
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