III. The Renaissance

Part 3: The problem of the circle

For centuries, the artist tried to depict depth on a two dimensional surface. Finally he found a way to accomplish it. Once Alberti came up with a solution, one can imagine how eager the artists were to implement the solution into their painting. Knowledge of perspective became a necessary tool in painting. "He who does not know geometry and is too afraid to learn it , would never become a great artist even with the biggest talent", says Alberti in example. For simplicity the painters only drew objects like cubes in perspective, since straight lines were easy to represent. Because of the irregular shape, human bodies were always drawn by hand. Applying perspective to humans would also have restricted the artistic expression. Even though circles are a basic geometric figure, they were too difficult to draw in perspective and were generally avoided.

Paolo Uccello's perspective construction for a garment for the head (after Kern)

It is Paolo Uccello (about 1400), one of the most important perspectivists of his time, who solved the problem of projecting a circle (after Kern). His object of interest was a bagel-shaped garment where the diameter of the radial cross section is smaller in the front. Since he knows well the projection of straight lines, he approximates the object by simple polygons. The outline consists of three pairs of regular 32-gones with their centers on top of each other and such that the cross section obtained by cutting the "bagel" radially is a regular hexagon. Connecting the vertices of the two outside 32-gones , one obtains squares and low pyramids with square basis "sit" on the frontal ones.

Go on to next section: Part 4: Application in Art

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