Painting - Measurement of the Earth (Eratosthenes)

The determination of the size and shape of the Earth has occupied philosophers from antiquity. Eratosthenes, a mathematician in the city of Alexandria in Egypt who lived from about 275 through 194 BC, proposed an ingenious way to measure the circumference of the Earth. It is illustrated by this painting. Eratosthenes claimed that the town of Syene (now Aswan) was directly south of Alexandria, and that the distance between the cities was known. Moreover, he reported that on a day when the vertical rod of a sundial cast no shadow at noon in Syene, the shadow cast by a similar rod at Alexandria formed an angle of 1/50 of a complete circle.

In the Crockett Johnson painting, the circle represents the Earth and the two line segments drawn from the center display the direction of the two rods. The two parallel lines represent rays of sunlight striking the Earth, the dark-purple region the shadowed area. The angle of the shadow equals the angle subtended at the center of the Earth, hence the circumference of the entire Earth can be computed when the angle and the distance of the cities is known.

Crockett Johnson's painting may be after a diagram from the book by James R. Newman entitled The World of Mathematics (p. 206), although the figure is not annotated. Newman published a brief extract describing ideas of Eratosthenes, based on a first century BC account by Cleomedes.

The Crockett Johnson painting is #15 in the series. It is marked on the back : Crockett Johnson 1966 (/) MEASUREMENT OF THE EARTH (/) (ERATOSTHENES).

Reference: O. Pederson and M. Phil, Early Physics and Astronomy (1974), p. 53.

Currently not on view