Painting - Archimedes Transversal | Smithsonian Institution

Object Details

Description: The construction of regular polygons using straightedge and compass alone is a problem that has intrigued mathematicians from ancient times. Crockett Johnson was particularly interested in the construction of regular seven-sided figures or heptagons, which require not only a compass but a marked straight edge. The mathematician Archimedes reportedly proposed such a construction, which was included in a treatise now lost. Relying heavily on Thomas Heath's Manual of Greek Mathematics, Crockett Johnson prepared this painting.; Archimedes had reduced the problem of finding a regular hexagon to that of finding two points that divided a line segment into two mean proportionals. He then used a construction somewhat like that of the painting to find a line segment divided as desired. Crockett Johnson's papers include not only photocopies of the relevant portion of Heath, but his own diagrams.; The painting is #104 in the series. It is in acrylic or oil on masonite., and has purple, yellow, green and blue sections. There is a black wooden frame. The painting is unsigned and undated. Relevant correspondence in the Crockett Johnson papers dates from 1974.; References: Heath, Thomas L., A Manual of Greek Mathematics (1963 edition), pp. 340–2.; Crockett Johnson, "A construction for a regular heptagon," Mathematical Gazette, 59 (March 1975): pp. 17–18.
Location: Currently not on view

ca 1974

Physical Description: masonite (substrate material); wood (frame material)
Measurements: overall: 83.4 cm x 83 cm x 4.5 cm; 32 13/16 in x 32 11/16 in x 1 3/4 in

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National Museum of American History

GUID (Link to Original Record): http://n2t.net/ark:/65665/ng49ca746a5-2084-704b-e053-15f76fa0b4fa