Painting - <I>Squared Lunes (Hippocrates Of Chios)</I>
date: label: date made
content: 1968
name: label: referenced
content: Hippocrates of Chios
label: painter
content: Johnson, Crockett
notes: label: Description
content: Classical Greek mathematicians were able to square all convex polygons. That is, given any polygon, they could produce a square of equal area in a finite number of steps using only a compass and a straight edge. Figures with curved sides proved more difficult. However, as this painting suggests, the mathematician Hippocrates of Chios (5th century BC) squared a lune, a figure bounded by arcs of two circle with different radii (lunes resemble quarter moons, hence the name). Finding the area of a lune in terms of a square might seem more difficult than squaring a circle, but the latter problem would prove intractable.
label: Description
content: The painting follows annotated figures in Evans G. Valens's <I>The Number of Things</I> (1964), p.103, which was part of Crockett Johnson's mathematical library. It corresponds to an early diagram in Valens's discussion of squaring the circle. According to Valens, Hippocrates began by arguing that the areas of similar segments of different circles are in the same ratio as the squares of their bases. Suppose an isosceles right triangle is inscribed in a semicircle of diameter c. Construct smaller semicircles of diameter a and b on the sides of the inscribed triangle. As the square of a plus the square of b equals the square of c, the area of the two smaller semicircles equals that of the large one. The proof goes on to consider the area of the two crescents and the triangle.
label: Description
content: Although Valens called the crescent moon shape a crescent, Crockett Johnson used the term lune. This probably indicates that he also read Herbert Westren Turnball “The Great Mathematicians” in The World of Mathematics, edited by James R. Newman (1956), where the term lune is used. Also, on page page 91 of Turnball’s article there is a diagram on which the painting could have been based.
label: Description
content: In this version of <I>Squared Lunes</I> Crockett Johnson uses brown, black, red, and white against a gray background. This oil painting is #67 in the series, and the first in the series with the title "Squared Lunes." It was completed in 1968 and is signed: CJ68. It is inscribed on the back: SQUARED LUNES (/) (HIIPPOCRATES OF CHIOS) (/) Crockett Johnson 1968. A related painting is #68 (1979.1093.43).
label: Location
content: Currently not on view
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
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: 1979.1093.42
label: accession number
content: 1979.1093
label: catalog number
content: 1979.1093.42
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Measurements
content: overall: 38.2 cm x 62.5 cm x 3.2 cm; 15 1/16 in x 24 5/8 in x 1 1/4 in