Penrose triangle

Penrose triangle

The Penrose triangle is the most famous and one of the simplest impossible figures. Its roots go back to 1934 when Oscar Reutersvärd made the first recognizable impossible triangle out of a strange two-dimensional representation of cubes; this artwork appeared on a Swedish postage stamp issued in 1982.


In 1954, Roger Penrose, after attending a lecture by the artist M. C. Escher, rediscovered the impossible triangle and drew it in its most familiar form, which he published in a 1958 article in the British Journal of Psychology, coauthored with his father Lionel.1 Penrose was also unfamiliar with the work of Reutersvärd, Piranesi, and others who had created impossible figures previously. Penrose's impossible triangle, unlike Reutersvärd's earlier version, was drawn in perspective, which added an additional size paradox to the object. In 1961, Escher, inspired by Penrose's version of the impossible triangle (he was sent a copy of the article by the Penroses), incorporated it into his famous lithograph "Waterfall."



1. Penrose, L.S., and Penrose, R. "Impossible Objects: A Special Type of Illusion," British Journal of Psychology, 49: 31, 1958.