Painting - Archimedes Transversal

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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
National Museum of American History
referenced
Archimedes
painter
Johnson, Crockett
Credit Line
Ruth Krauss in memory of Crockett Johnson
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
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Art
Crockett Johnson
ca 1974
Object Name
painting
ID Number
1979.1093.71
catalog number
1979.1093.71
accession number
1979.1093