Impossible Triangle

By Stephen L. Macknik and Susana Martinez-Conde

The impossible triangle (also called the Penrose Triangle or the “tribar”) was first created in 1934 by Oscar Reutersvärd. Penrose, the famous mathematical physicist, attended a lecture by the artist M. C. Escher in 1954, which inspired him to rediscover the impossible triangle. Penrose (who at the time was unfamiliar with the work of Reutersvärd, Piranesi and other previous discoverers of the impossible triangle) drew illusion in its now most familiar form, and published his observations in the British Journal of Psychology in 1958, in an article coauthored with his father, Lionel. In 1961 the Penroses sent a copy of the article to Escher, who incorporated the effect into "Waterfall," one of his most famous lithographs.

Another impossible triangle (now in Ophoven, Belgium) at right, with a different resolution altogether. Again, the viewer’s location relative to the object is critical. Now you know why there are various physical ways to achieve any particular impossible object.

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