# Ivars Peterson's MathTrek

May 8, 2006

## Quilting Pi

When John Sims contemplates a number, he sees color and shape. And an intriguing, enigmatic number such as pi, the ratio of a circle's circumference to its diameter, conjures up vivid patterns that belong on quilts.

Starting with 3.14159265, the decimal digits of pi run on forever, and there's no discernible pattern to ease the task of compiling (or memorizing) these digits. Computer scientists have so far succeeded in computing 1,241,100,000,000 decimal digits of pi.

Both a mathematician and an artist, Sims taught for many years at the Ringling School of Art and Design in Sarasota, Fla. He's passionately interested in the collision of mathematical ideas and visual culture.

Pi is one of the few mathematical constants that have successfully entered the pop-culture psyche, Sims notes. Pi has appeared as the title of movie, for instance, and as the name of a perfume.

Several years ago, Sims created a visualization of pi's digits in a digital video format—with music by Frank Rothkamm and the participation of Paul D. Miller, who is better known on the New York City scene and elsewhere as Dj Spooky. You can find this creation at the John Sims Project Web site (http://www.johnsimsprojects.com/). In this visualization, each of the digits from 0 to 9 is represented by its own color on a vast grid of squares.

Working in base 2 and using the colors black and white, Sims then created "Black White Pi". In base 3, using red, white, and blue, he made "American Pi."

From left to right, "Seeing Pi," "American Pi," and "Black White Pi."
Courtesy of John Sims

A second pi-based project involved a collaboration with conceptual artist Sol LeWitt. LeWitt's instructions were to put 1,000 straight lines inside a square. Sims achieved that result by dividing each side of the square into 10 parts (like the axes of a graph), labeling the divisions from 0 to 9, and drawing lines from a division on one side to a division on an adjacent side. The lines followed successive digits of pi from side to side, starting at the top and moving in a clockwise direction until the wall drawing had 1,000 lines. Sims' former student, Brandon Styza, actually drew the lines. The result formed the basis for a LeWitt wall drawing in the math lounge at Wesleyan University in Middletown, Conn. (see http://www.math.wesleyan.edu/).

This year, before heading for New York City, Sims completed a number of pi works, including several quilts that were constructed by an Amish quilting group in Sarasota. These artworks were on display at Sarasota's mack b gallery.

Sims started out with a drawing of pi's decimal digits on a square grid, with successive digits forming a clockwise spiral from the center.

:A square spiral of the digits of pi.
Photo by Tobey Albright

In the gallery, this drawing was displayed with a phonograph that played a recording of Sims reciting the digits of pi in order. A second track presented the digits in German.

With each digit from 0 to 9 mapped to a different color (but not black or white), the central portion of the drawing was then converted into a striking, square quilt of colored patches, with a black border. Sims calls the creation "Pi sans Salt and Pepper."

"Pi sans Salt and Pepper" by John Sims. The square quilt is 8 feet wide.
Photo by Tobey Albright

In a variation on this pi-based theme, another quilt designed by Sims features several, differently color-coded representations of pi. It's called "Civil Pi Movement."

In this pi-based quilt, called "Civil Pi Movement," the upper left unit shows the first 36 binary digits of pi (0 = white and 1 = black) and the lower right unit reverses the color scheme. The upper right unit shows the first 36 ternary digits of pi (0 = dark blue, 1 = red, and 2 = white) and the lower left unit uses a different color scheme (0 = green, 1 = red, and 2 = black). The center unit matches the center of "Pi sans Salt and Pepper." The square quilt is 8 feet wide.
Photo by Tobey Albright

"The mathematical art that I seek to develop combines mathematical language and analysis with the expressiveness and creativity of the process to make expressive visual theorems," Sims says. "To see mathematically, one draws from creativity and intuition, as in the case with the art process itself."

Check out Ivars Peterson's MathTrek blog at http://blog.sciencenews.org/. He was a Web page at http://ivarspeterson.googlepages.com/.

References:
John Sims has a Web site at http://www.johnsimsprojects.com/.

Peterson, I. 2002. A trillion pieces of pi. MAA Online (Dec. 16).

______. 2002. Fractal roots and artful math. MAA Online (June 10).

______. 2001. Fragments of Infinity: A Kaleidoscope of Math and Art. New York: Wiley. See http://ivarspeterson.googlepages.com/art.

______. 2001. Pi à la mode. Science News 160(Sept. 1):136-137. Available at http://www.sciencenews.org/articles/20010901/bob9.asp.

______. 2000. Puzzling lines. MAA Online (June 12).

______. 2000. Sliding pi. MAA Online (June 5).