Painting - <I>Construction of a Heptagon</I>
date: label: date made
content: ca 1975
name: label: painter
content: Johnson, Crockett
notes: label: Description
content: This is one of three very similar Crockett Johnson paintings closely related to the construction of a side of an inscribed regular heptagon which the artist 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.
label: Description
content: Crockett Johnson described the construction of his isosceles triangle in the diagram shown. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the largest triangle in the painting is triangle is ABF in the figure, with vertex angle equal to one seventh of pi. This angle is inscribed in the large circular arc KDC. The side of the heptagon is the chord KC.
label: Description
content: This version of Crockett Johnson's construction of a heptagon is #115 in the series. It has a dark blue background and a wood and metal frame. The painting is an oil or acrylic on masonite. The work is unsigned. See also #108 (335571) and #117 (1979.1093.79).
label: Description
content: References: 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: 1979.1093.77
label: accession number
content: 1979.1093
label: catalog number
content: 1979.1093.77
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: 125 cm x 69 cm x 3.5 cm; 49 3/16 in x 27 3/16 in x 1 3/8 in