Capturing Infinity

The Circle Limit Series of M.C. Escher

By Thomas Wieting

In July 1960, shortly after his 62nd birthday, the graphic artist M.C. Escher completed Angels and Devils, the fourth (and final) woodcut in his Circle Limit Series. I have a vivid memory of my first view of a print of this astonishing work. Following sensations of surprise and delight, two questions rose in my mind. What is the underlying design? What is the purpose? Of course, within the world of Art, narrowly interpreted, one might regard such questions as irrelevant, even impertinent. However, for this particular work of Escher, it seemed to me that such questions were precisely what the artist intended to excite in my mind.

In this essay, I will present answers to the foregoing questions, based upon Escher’s articles and letters and upon his workshop drawings. For the mathematical aspects of the essay, I will require nothing more but certainly nothing less than thoughtful applications of straightedge and compass.