Painting - Square Roots to Sixteen (Theodorus of Cyrene)

Object Details

referenced

Theodorus of Cyrene

painter

Johnson, Crockett

Description

Greek mathematicians knew that numbers could not always be represented as simple ratios of whole numbers. They devised ways to describe them geometrically. The title of this painting refers to Theodorus of Cyrene (about 465–398 BC), a Greek geometer who, according to the Greek mathematician Theaetetus (about 417–369 BC), constructed the square roots of the numbers from 3 through 17. Crockett Johnson's painting follows a diagram in Evans G. Valens's The Number of Things that stops with the square root of 16.

The construction of this oil or acrylic painting, #45 in the series, begins with a vertical line segment of length one. Crockett Johnson then drew a right angle at the base of the segment and an adjacent line with length one. From the Pythagorean theorem, it follows that a line from the center of the spiral has length equal to the square root of 2. The construction was continued until the last hypotenuse displayed length equal to the square root of 16.

The painting, which looks like a seashell, shows a specific color pattern. The three dark gray triangles have hypotenuses whose lengths are whole numbers (the square roots of 4, 9, and 16). The six white triangles have hypotenuses whose lengths are irrational and are square roots of even integers. Finally, the six tan triangles have hypotenuses whose lengths are irrational and the square roots of odd integers.

The painting dates from 1967 and is signed: CJ67. It is marked on the back: Crockett Johnson (/) SQUARE ROOTS TO SIXTEEN (/) (THEODORUS OF CYRENE).

Location

Currently not on view

Credit Line

Ruth Krauss in memory of Crockett Johnson

1967

ID Number

1979.1093.32

catalog number

1979.1093.32

accession number

1979.1093

Object Name

painting

Physical Description

masonite (substrate material)

wood (frame material)

Measurements

overall: 108 cm x 84 cm x 3.2 cm; 42 1/2 in x 33 1/16 in x 1 1/4 in

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Crockett Johnson

Art

National Museum of American History

Record ID

nmah_694656

Metadata Usage (text)

CC0

GUID (Link to Original Record)

http://n2t.net/ark:/65665/ng49ca746a5-3df3-704b-e053-15f76fa0b4fa