Painting - Construction of Heptagon

Object Details

painter

Johnson, Crockett

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

Credit Line

Ruth Krauss in memory of Crockett Johnson

ca 1975

ID Number

1979.1093.79

accession number

1979.1093

catalog number

1979.1093.79

Object Name

painting

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

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694703

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-171b-704b-e053-15f76fa0b4fa