Painting - <I>Biblical Squared Circles</I>
date: label: date made
content: ca 1972
name: label: painter
content: Johnson, Crockett
notes: label: Description
content: This painting, #92 in the series, relates to a verse in the Old Testament (I Kings, Chapter VII, Verse 23) which states, "Also he made a molten sea of ten cubits brim to brim, round in compass, . . . and a line of thirty cubits did compass it round about." This verse tells us that the circular sea had a circumference of 30 cubits and a diameter of 10 cubits. Because the value of pi is defined as the ratio of a circle’s circumference to its diameter (pi = c/d), the ancient Hebrew text uses 30/10 = 3 as the value for pi.
label: Description
content: To illustrate this value of pi, Crockett Johnson inscribes the six-pointed Star of David within a circle. The curve joining two opposite points of the star (point C and point F in his figure) serves as a reminder of how to construct a six-pointed figure inside a circle. Furthermore, he inscribes a second, smaller circle inside the hexagon created by the six-pointed star.
label: Description
content: In this painting, it is assumed that the value of pi is 3. There are several relationships in the painting that involve this number. The inner circle has radius 1/2 and the outer circle has radius 1. Thus, the smaller circle has circumference pi and the larger circle has area pi. Triangle ABC in Crockett Johnson's figure is a 30-60-90 triangle with AC = 1, AB = 2, and CB equals the square root of 3. It follows that CD, BD, EA, EF, and AF also equal the square root of 3. The Star of David is composed of two overlapping equilateral triangles (triangles AEF and BCD in the figure). Triangle AEF has altitude AH = 3/2 and triangle BCD has altitude BG = 3/2. Thus, the sum of their altitudes is AH + BG = 3. It is also interesting to note that, although the dotted lines in the accompanying figure are not present in the painting, the area of the square created by the dotted corners equals three.
label: Description
content: In reference to this painting, Crockett Johnson wrote, "Each of the six sides of the two equilateral triangles equaled the square root of the area of the outer circle and the square root of the circumference of the inner circle; together the altitudes of the male and female triangles equaled the area of the outer circle and the circumference of the inner circle. Of course both of these circular dimensions are pi, but ecclesiastically pi equaled 3."
label: Description
content: The artist chose several tints and shades of blue for this painting. The illustration is darker underneath the curve from C to F than it is above, and the transition between each tint and shade is subtle. The choice of this one, “cool” color evokes a feeling of tranquility.
label: Description
content: This work was painted in oil on masonite, and has a wood and metal frame. It is unsigned and its date of completion is unknown.
label: Description
content: Reference: Biblical Squared Circles, 1979.3083.02.09, Crockett Johnson Collection.
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Crockett Johnson
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content: Art
label: Exhibition
content: NMAH Board Room Entry
label: Exhibition Location
content: National Museum of American History
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: 1979.1093.61
label: catalog number
content: 1979.1093.61
label: accession number
content: 1979.1093
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Physical Description
content: metal (frame material)
label: Measurements
content: overall: 64 cm x 64 cm x 3.2 cm; 25 3/16 in x 25 3/16 in x 1 1/4 in