## Painting - *Archimedes Transversal*

- 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