Painting - Construction of a Heptagon

  • images for Painting - <I>Construction of a Heptagon</I>-thumbnail 1
  • images for Painting - <I>Construction of a Heptagon</I>-thumbnail 2
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 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 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.
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).
References: Crockett Johnson, “A Construction for a Regular Heptagon,” Mathematical Gazette, 1975, vol. 59, pp. 17–21.
Currently not on view
National Museum of American History
Johnson, Crockett
Credit Line
Ruth Krauss in memory of Crockett Johnson
Physical Description
masonite (substrate material)
wood (frame material)
metal (frame material)
overall: 125 cm x 69 cm x 3.5 cm; 49 3/16 in x 27 3/16 in x 1 3/8 in
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Crockett Johnson
ca 1975
Object Name
ID Number
accession number
catalog number