Oscar Reutersvärd

Oscar Reutersvärd (1915–2002) is one of those figures whose priority is well documented but whose fame never caught up with it. A Swedish artist who also taught art history, he is credited with the earliest known drawing of the impossible triangle: three beams joined at right angles that form a closed loop which could never exist in three dimensions.

The 1934 drawing

By his own account, Reutersvärd drew the figure in 1934, at the age of 18, while sketching an arrangement of cubes, and only gradually realised he had drawn something impossible (Ernst, 1986). He went on to explore the idea for the rest of his life, producing thousands of impossible figures made of cubes, rings, staircases and lattices, usually drawn in his distinctive style of flat, evenly shaded blocks without converging perspective. The style makes the impossibility read less like a trick of depth and more like a puzzle in graphic design.

His drawing came more than twenty years before the version that made the figure famous, published by Lionel and Roger Penrose in 1958 (Penrose & Penrose, 1958). The Penroses arrived at it independently. Credit is fairly shared: Reutersvärd for drawing it first, and the Penroses for analysing it as a problem of perception, which brought it into psychology and gave it the name most people know.

Recognition

Outside Sweden, Reutersvärd remained little known for much of the twentieth century. At home, recognition came: in 1982, Sweden issued postage stamps based on his impossible figures, and he became known there as the father of the impossible figure. Internationally, his name still tends to be overshadowed by the Penroses and by M. C. Escher, even though Escher's impossible prints were based on the Penroses' paper rather than on Reutersvärd's drawings.

Why it matters to perception

Reutersvärd's work shows a purely geometric curiosity being discovered by an artist working from intuition, decades before psychologists used the same idea to study how the visual system joins local depth cues into a single three-dimensional object. It also shows that impossible figures aren't a single image but a whole family. The Penrose triangle page has a model built from cubes in Reutersvärd's manner: a real object that becomes his impossible triangle from exactly one direction.