Painting - <I>Squares of a 3-4-5 Triangle in Scalene Perspective (Dürer)</I>
date: label: date made
content: 1965
name: label: referenced
content: Duerer, Albrecht
label: painter
content: Johnson, Crockett
notes: label: Description
content: This painting, while similar in subject to the painting entitled <I>Perspective (Alberti)</I>, depicts three planes perpendicular to the canvas. These three planes provide a detailed, three-dimensional view of space through the use of perspective. Three vanishing points are implied (though not shown) in the painting, one in each of the three planes.
label: Description
content: The painting shows a 3-4-5 triangle surrounded by squares proportional in number to the square of the side. That is, the horizontal plane contains nine squares, the vertical plane contains sixteen squares, and the oblique plane, which represents the hypotenuse of the 3-4-5 triangle, contains twenty-five squares. This explains the extension of the vertical and oblique planes and reminds the viewer of the Pythagorean theorem.
label: Description
content: The title of this painting points to the role of the German artist Albrecht Dürer (1471–1528) in creating ways of representing three-dimensional figures in a plane. Dürer is particularly remembered for a posthumously published treatise on human proportion. In his book entitled <I>The Life and Art of Albrecht Dürer</I>, art historian Erwin Panofsky explains that the work of Dürer with perspective demonstrated that the field was not just an element of painting and architecture, but an important branch of mathematics.
label: Description
content: This construction may well have originated with Crockett Johnson. However, he may have been influenced by Figure 1 (p. 604) and Figure 3 (p. 608) in Panofsky’s article on Dürer as a Mathematician in The World of Mathematics, edited by James R. Newman (1956). Johnson did not annotate either of these diagrams. The oil painting was completed in 1965 and is signed: CJ65. It is #8 in his series of mathematical paintings.
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: 1979.1093.04
label: catalog number
content: 1979.1093.04
label: accession number
content: 1979.1093
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: wood (frame material)
label: Physical Description
content: masonite (substrate material)
label: Measurements
content: overall: 82 cm x 65 cm x .6 cm; 32 5/16 in x 25 9/16 in x 1/4 in