circles, tangents, and conceptual art

The math department at Smith College recently acquired a new art installation: Sol LeWitt’s Wall Drawing #139 (Grid and arcs from the midpoints of four sides). This piece was a gift to the Smith museum, and was first installed there in 2008. It is an example of “conceptual art,” of which LeWitt was a major exponent during the 20th century. While conceptual art was/is a large movement, of which I am almost completely ignorant, in this case (like many others of LeWitt’s wall drawings) it means that the art resides in a concept—more precisely, a set of instructions—which is created by the artist and carried out by a team in each physical location. This is analogous to the creation of music, with the artist playing the role of the composer and the installation team acting like the musicians, who must take the artist’s instructions and interpret them in their particular setting.

(You can click on each image below for a full-sized version.)

 In this case, the directions (paraphrased) are as follows:

• Draw a grid of lines evenly spaced 1 inch apart over the dedicated wall space.
• Draw circles centered at the midpoint of each of the four sides, with radii increasing by 1 inch, all the way across the wall.

Here are the four midpoints:



You can learn more about the original installation at the museum from a video. I just wanted to make these pictures available and to highlight the possibility of asking innumerable mathematical questions about this piece. For instance, the grid and circles produce varying patterns and densities throughout the space:


Can you tell where each of these pictures was taken? In the center of the piece, many coincidences appear and tangencies among the circles and the grid lines become evident:


The installation was done by three Smith students in art and math, directed by a professional installer from the LeWitt studio over the course of nine days in January. At a presentation last week, the students described the exactness and concentration that this project required, as well as certain accommodations that had to be made—for example, not all of the wall edges are perfectly straight, and so they had to determine how to adjust the grid, and what points to use as the midpoints. Apparently one circle has a radius that is slightly too large, because of slackness in the compass they were using. (I haven’t yet found where this circle is.) Clearly there is an interesting interplay between form and accident (in the Aristotelian sense), leading to all sorts of philosophical questions that I’m not up to expounding at the moment.

This is the first of LeWitt’s works that I have encountered. I’m sure others have plenty of mathematical material to explore, as well.