Escher and the Möbius Strip

Abstract

Escher was once quoted as saying: “In 1960 I was exhorted by an English mathematician (whose name I do not call to mind) to make a print of a Möbius strip. At that time I scarcely knew what it was”.¹ He responded to this challenge by producing two images that became famous: Möbius Strip I and Möbius Strip II, which I’ve reproduced here. In the first of these woodcuts, which seems to depict three snakes biting each others’ tails, Escher invites us to follow the line of the snakes. What we discover, to our surprise, is that the three reptiles are all on the same surface even though they appear to be following two distinct orbits. In the second woodcut, Möbius Strip II, we see nine ants all crawling in the same direction. This time Escher asks us to follow their path and confirm that it is indeed a path without end, because no matter which starting point you choose, you always end up at the same point. The ants appear to be crawling on two separate sides of a single surface, but ultimately each of them travels the entire length of the surface on which they are crawling. In both these images the paths are endless.