Painting - <I>Construction of Heptagon</I>
date: label: date made
content: ca 1975
name: label: painter
content: Johnson, Crockett
notes: label: Description
content: Three very similar paintings in the Crockett Johnson collection are closely related to the the construction of a side of an inscribed regular a heptagon which he published in <I>The Mathematical Gazette</I> in 1975. The paper presents a way of producing an isosceles triangle with angles in the ratio 3:3:1, so that the smallest angle in the triangle is π/ 7. This angle is then inscribed in a large circle, and intercepts an arc length of π/7. A central angle of the same circle intercepts twice the angle, that is to say 2π/7, and the corresponding chord the side of an inscribed heptagon. Crockett Johnson described the construction of his isosceles triangle in the diagram reproduced. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the triangle is ABF. Three of the four light-colored sections of the painting highlight important points in the construction. The critical steps are drawing a perpendicular bisector to the line segment BF, marking off an arc of radius equal to the √(2) with center F, and measuring the unit length AO along a marked straightedge that passes through B and intersects the perpendicular bisector at A. Finally, one finds the side of the regular inscribed heptagon.
label: Description
content: <I>Construction of Heptagon</I> is #117 in the series. The oil painting on masonite is in shades of purple, cream, turquoise, and black. It has a black wood and metal frame. The work is unsigned. The surface appears damaged, perhaps from water. See also #115 (1979.1093.77) and #108 (335571).
label: Description
content: Reference: Crockett Johnson, “A Construction for a Regular Heptagon,” <I>Mathematical Gazette</I>, 1975, vol. 59, pp. 17–21.
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: 1979.1093.79
label: accession number
content: 1979.1093
label: catalog number
content: 1979.1093.79
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Physical Description
content: metal (frame material)
label: Measurements
content: overall: 49 in x 42 15/16 in x 1 3/16 in; 124.46 cm x 109.00004 cm x 2.99999 cm