The Development of Geometry, II

Abstract

THE LAWS OF PERSPECTIVE DRAWING—the technique used to portray three dimensions on a two dimensional surface—have been studied by artists since the Stone Age. For example, a fifteen thousand year old etching of a herd of reindeer on a bone fragment discovered by archaeologists creates the impression of distance by displaying the legs and antlers as if seen beyond the fully sketched animals of the foreground. The main perspective problem encountered by Egyptian artists was the portrayal of a single important object with the necessary dimension of depth: this was achieved in an ingenious manner by drawing a combination of horizontal and side view. Thus, for instance, in drawing a Pharaoh carrying a circular tray of sacrificial offerings, the top view of the tray is shown in half display by means of a semicircle, and on this half-tray is presented the sacrificial food as it would appear from above. This stylized method of expressing a third dimension persisted in Egyptian drawing for three thousand years. In America, an arresting method of achieving this effect was created by northwest Indian artists who, in their drawings of persons or animals, present views of both front and left- and right hand sides. The figures are drawn as if split down the back and flattened like a hide, with the result that each side of the head and body becomes a profile facing the other. Landscapes drawn by Chinese artists create the impression of space and distance by skillful arrangement of land, water and foliage. In drawing buildings, however, it was necessary to display the parallel horizontal lines of the construction, and for this the technique of isometric drawing was used. This is a simulation of perspective drawing in which parallel lines are drawn parallel, instead of converging as in true perspective.