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Math in Art

A Unique Perspective
René Magritte<br>Belgian, 1898-1967<br><i>Promenades of Euclid</i>, 1955<br>Oil on canvas<br>Minneapolis Institute of Arts<br>The William Hood Dunwoody Fund
zoom René Magritte
Belgian, 1898-1967
Promenades of Euclid, 1955
Oil on canvas
Minneapolis Institute of Arts
The William Hood Dunwoody Fund


René Magritte’s Promenades of Euclid, painted in 1955, is a wonderful example of one-point linear perspective. Invented during the Renaissance, over five hundred years ago, linear perspective is a simple method of using lines to give an illusion of depth.

Renaissance artists strove to make their paintings look as real as possible. This prompted them to use geometry to help fool the eye into seeing depth beyond the painting’s flat surface. By having lines come together at a “vanishing point,” they developed linear perspective as a way to make painted landscapes and architecture appear solid and three-dimensional.

An artist using linear perspective begins by establishing a horizon line. This is the meeting place of earth and sky—where the sun rises and sets and the landscape recedes beyond what the eye can see. Lines in the artwork converge at a single point on the horizon, the way railroad tracks appear to meet in the distance. Objects closer to the viewer are shown as larger than those farther away, just as they look in nature.

In his Promenades of Euclid—a clever painting within a painting—Magritte used linear perspective for the promenade (walkway) and the cone-shaped tower that mimics it. He created a trompe l’oeil (French for “fool the eye”) that makes us wonder whether the scene outside the window is the same as that painted on the canvas which is blocking the view.

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1. Another way to show distance is aerial perspective. By painting the mountains farthest away in less detail and partly hidden by clouds, this Chinese artist created the illusion of distance. Magritte also used aerial perspective, painting the background in bluish shades and with less precision.
Wang Shih-min, Landscape after Huang Kung-wang, 1670, ink and colors on paper, Minneapolis Institute of Arts, gift of Ruth and Bruce Dayton
2. Before the Renaissance, in medieval times, artists had different aims. The designers of medieval textiles like this one did not use mathematical perspective but instead crowded the figures into a space that seems too small to hold them all.
Flemish, Esther and Ahasuerus, 1460-85, wool, silk, Minneapolis Institute of Arts, gift of Mrs. C. J. Martin for the Charles Jairus Martin Memorial Collection
3. Magritte also used geometry to create a convincingly solid cylindrical tower with a cone-shaped top.


March 2010