Painting - <I>Duality (Pascal-Brianchon)</I>
date: label: date made
content: 1966
name: label: referenced
content: Pascal, Blaise
label: referenced
content: Brianchon, Charles Julien
label: painter
content: Johnson, Crockett
notes: label: Description
content: As a 21-year-old student, the Frenchman Charles Jules Brianchon (1785–1864) discovered that in any hexagon circumscribed about a conic section (such as a circle), the three lines that join opposite diagonals meet in a single point. He also pointed out connections between his result and Pascal's theorem concerning the points of intersection of opposite sides of a hexagon inscribed in a conic section.
label: Description
content: In the painting, a hexagon (only the vertices are shown) is inscribed in a circle. Three diagonal lines (edges of the gray and black polygon) are collinear. The line in question is the line joining the points of intersection, white on one side and purple on the other. Crockett Johnson's painting closely resembles a diagram of A. S. Smogorzhevskii in which Brianchon's theorem is applied to a proof of Pascal's theorem.
label: Description
content: The painting on masonite is #81 in the series. It has a purple background and a black wooden frame. It is signed: CJ66.
label: Description
content: References: A. S. Smogorzhevskii, <I>The Ruler in Geometrical Constructions</I> (1961), p. 37. This volume was in Crockett Johnson's library. The figure is not annotated.
label: Description
content: Carl Boyer and Uta Merzbach, <I>A History of Mathematics</I> (1991), p. 534.
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: 1979.1093.53
label: catalog number
content: 1979.1093.53
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: Measurements
content: overall: 65 cm x 65 cm x 1.3 cm; 25 9/16 in x 25 9/16 in x 1/2 in