Quinze variations sur un même thème (Fifteen Variations on a Theme)

Max Bill established himself as the preeminent Swiss designer of the mid-20th century with both his theoretical writing and his clean designs. As he explains in the introduction to this book, understanding the logic of a composition enables an artist to maximize the “pleasure” of creation. Accordingly, Bill presents 15 examples illustrating how an equilateral triangle and an equilateral octagon can interact graphically, providing a detailed explanation for how he generated each unique configuration. The variety is stunning as successive diagrams show how basic geometric forms can explode into new patterns through overlapping, selectively reducing, or building up lines and playing with negative space. This portfolio is one of 10 retained by the artist, and it bears an inscription to Bill’s friend Marcel Duchamp revealing that it was gifted to him soon after its publication. It’s tantalizing to speculate that Duchamp’s interest in optics, as shown in, for example, Composition with Circles (1919/1950; 1971.924) and 12 Rotoreliefs (1953, 2019.157) may have prompted some fruitful exchanges between the artists on the topic of mathematics, perception and design.