Painting - Construction of a Heptagon

Description:

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.

Date Made: ca 1975

Painter: Johnson, Crockett

Location: Currently not on view

See more items in: Medicine and Science: Mathematics, Science & Mathematics, Crockett Johnson, Art

Exhibition:

Exhibition Location:

Credit Line: Ruth Krauss in memory of Crockett Johnson

Data Source: National Museum of American History

Id Number: 1979.1093.77Accession Number: 1979.1093Catalog Number: 1979.1093.77

Object Name: painting

Physical Description: masonite (substrate material)wood (frame material)metal (frame material)Measurements: overall: 125 cm x 69 cm x 3.5 cm; 49 3/16 in x 27 3/16 in x 1 3/8 in

Guid: http://n2t.net/ark:/65665/ng49ca746a5-1719-704b-e053-15f76fa0b4fa

Record Id: nmah_694701

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.