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.
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)
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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Medicine and Science: Mathematics
Science & Mathematics
Crockett Johnson
ca 1974
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