Painting -<I>Approximation of Pi to .0001</I>
date: label: date made
content: 1970-1975
name: label: painter
content: Johnson, Crockett
notes: label: Description
content: 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.
label: Description
content: 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.
label: Description
content: A diagram from Crockett Johnson's papers presents the mathematics of his construction.
label: Description
content: 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 right side, 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 tleft side are in dark purple and black.
label: Location
content: Currently not on view
setName: label: See more items in
content: Medicine and Science: Mathematics
label: See more items in
content: Science & Mathematics
label: See more items in
content: Crockett Johnson
label: See more items in
content: Art
creditLine: label: Credit Line
content: Ruth Krauss in memory of Crockett Johnson
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1979.1093.68
label: catalog number
content: 1979.1093.68
label: accession number
content: 1979.1093
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Measurements
content: overall: 61 cm x 82 cm x .6 cm; 24 in x 32 5/16 in x 1/4 in
label: Measurements
content: overall: 25 in x 2 in x 34 in; 63.5 cm x 5.08 cm x 86.36 cm