# Painting - Construction of Heptagon

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Description
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 The Mathematical Gazette 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.
Construction of Heptagon 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).
Reference: Crockett Johnson, “A Construction for a Regular Heptagon,” Mathematical Gazette, 1975, vol. 59, pp. 17–21.
Location
Currently not on view
Object Name
painting
ca 1975
painter
Johnson, Crockett
Physical Description
masonite (substrate material)
wood (frame material)
metal (frame material)
Measurements
overall: 49 in x 42 15/16 in x 1 3/16 in; 124.46 cm x 109.00004 cm x 2.99999 cm
ID Number
1979.1093.79
accession number
1979.1093
catalog number
1979.1093.79
Credit Line
Ruth Krauss in memory of Crockett Johnson
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Art
Crockett Johnson
Data Source
National Museum of American History
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