Painting - <I>Pencil of Ratios (Monge)</I>
date: label: date made
content: 1966
name: label: referenced
content: Monge, Gaspard
label: painter
content: Johnson, Crockett
notes: label: Description
content: The history of projective geometry begins with the work of the French mathematician Gerard Desargues (1591–1661). During his lifetime his work was well known in some mathematical circles, but after his death, his contributions to the field were largely forgotten. When Gaspard Monge (1746–1818) and his student, Jean-Victor Poncelet (1788–1867) began their studies of projective geometry, they were largely unaware of the work of Desargues. This may be why Crockett Johnson included Monge's name as opposed to Desargues' in this painting's title.
label: Description
content: One of the fundamental concepts of projective geometry, which was touched upon, but not fully understood, by the Greeks, is that of a cross-ratio, or "ratio of ratios." It is the topic of Johnson's painting. If points A, B, C, and D on line l are projected from point O, and if the line l’ crosses the four projected line segments, then the ratio of ratios (A’C’/C’B’)/(A’D’/ D’B’) of the corresponding points A’,B’,C’, and D’ is the same as the ratio of ratios (AC/CB)/(AD/DB). Thus, a cross-ratio is a projective invariant for all line segments l’.
label: Description
content: The artist may have received inspiration for this painting from his copy of James R. Newman's <I>The World of Mathematics</I> (1956), p. 632. The figure is found there in an article by Morris Kilne entitled "Projective Geometry." This figure is not annotated, and the painting flips Kline's image.
label: Description
content: Crockett Johnson chose purple, white, black, and brown to color this work. He executed the projection in three tints of purple and one shade of white. The background, which is divided by line l’, was executed in black and brown.
label: Description
content: <I>Pencil of Ratios</I>, an oil painting on masonite, is #18 in the series. It was completed in 1966 and is signed: CJ66. It is signed on the back: Crockett Johnson 1966 (/) PENCIL OF RATIOS (MONGE). The painting is unframed.
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: 1979.1093.12
label: catalog number
content: 1979.1093.12
label: accession number
content: 1979.1093
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Measurements
content: overall: 60.5 cm x 61 cm x .5 cm; 23 13/16 in x 24 in x 3/16 in