Painting - Duality (Pascal-Brianchon)

Object Details

referenced

Pascal, Blaise

Brianchon, Charles Julien

painter

Johnson, Crockett

Description

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

Credit Line

Ruth Krauss in memory of Crockett Johnson

1966

ID Number

1979.1093.53

catalog number

1979.1093.53

accession number

1979.1093

Object Name

painting

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

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694677

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-2335-704b-e053-15f76fa0b4fa