Painting - Duality (Pascal-Brianchon)

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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.
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.
The painting on masonite is #81 in the series. It has a purple background and a black wooden frame. It is signed: CJ66.
References: A. S. Smogorzhevskii, The Ruler in Geometrical Constructions (1961), p. 37. This volume was in Crockett Johnson's library. The figure is not annotated.
Carl Boyer and Uta Merzbach, A History of Mathematics (1991), p. 534.
Location
Currently not on view
National Museum of American History
referenced
Pascal, Blaise
Brianchon, Charles Julien
painter
Johnson, Crockett
Credit Line
Ruth Krauss in memory of Crockett Johnson
Physical Description
masonite (substrate material)
wood (frame material)
Measurements
overall: 65 cm x 65 cm x 1.3 cm; 25 9/16 in x 25 9/16 in x 1/2 in
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Art
Crockett Johnson
1966
Object Name
painting
ID Number
1979.1093.53
catalog number
1979.1093.53
accession number
1979.1093