# The Geometry of Quilting

GATLIN NEWHOUSE ’19 FOR THE QUEST

### Prof. Irena Swanson ’87 adds a new twist to a mathematical art form

###### By Katelyn Best ’13

Irena's quilts
Photos by Alex Krafcik ’15

Grids of zigzaggy diamonds in blues and greens. Furrows of autumnal squares. Triangles like a cubist pumpkin patch. Quilts of every description cover practically every surface of the home of Prof. Irena Swanson ’87 [math 2005–], immersing the visitor in a dizzying wash of color and pattern.

Before you explore, however, you had better take off your shoes—this is a shoe-free house, she explains, handing me a pair of buckskin moccasins. It’s a fitting introduction to a professor who seems always to be engaging both halves of her brain, the logical and the creative, the orderly and the chaotic.

Prof. Swanson’s professional life revolves around ideas in higher mathematics such as binomial ideals, Frobenius numbers, and hypermatrices. But she is also passionate about quilting, and has spent the last several years developing an innovative technique called tube piecing. In short, tube piecing is a method of assembling rows of geometric shapes—rectangles, parallelograms, or triangles—that’s drastically more efficient and precise than the standard technique of cutting up pieces of fabric and sewing them together individually. “For triangles, traditional piecing uses at least four times as many seams as my method,” she explains.

The basic idea is simple. She sews together strips of fabric in alternating light and dark colors, slightly offset so that they form a parallelogram with vertical stripes. She then sews the long edges of the parallelogram together to make a tube. Next, the tube is cut into rings, perpendicular to the seams, forming a series of quadrilaterals. These rings are then rotated and resewn so that each light quadrilateral is positioned above a dark one.

Armed with this technique—building a tube, cutting it into sections, and reassembling the sections—the quilter can construct an astonishing variety of patterns. If you choose your colors right, you can produce triangles, hexagons, zigzags, or swirls. Swanson has sewn one quilt composed of rows of dazzling blue parallelograms at varying angles, giving the impression of ocean waves.

Conceptually, tube piecing is an extension of strip piecing, a technique developed by Ernest Haight in the 1960s and ’70s. While strip piecing is a vast improvement over traditional piecing, tube piecing is still more efficient, with fewer seams and less waste. If strip piecing is the printing press, tube piecing is the laser printer.

The idea for tube piecing was born of frustration. Swanson was making a baby quilt consisting of a checkerboard pattern rotated 45°. “It was so much cutting and sewing, and there was so much waste at the end,” she says. “I just thought, ‘I could do this better.’”

Fifty, soft-spoken with a gentle accent, Swanson grew up on a farm in Yugoslavia, in what would become Slovenia. Her parents, born a decade before World War II tore their country apart, didn’t get a good education, but Irena describes them as whip-smart nonetheless, saying, “My mother can compute a lot of things in her head that I would reach out for a pencil or paper to do.” Her father taught her to play chess, and she became a formidable and unpredictable player. “I won many games,” she says, “because my theoretically prepared opponents were not prepared for spontaneous, thought-out-in-the-moment moves.”

In high school, she spent a year in Utah, where she made her first quilt. Her host mother’s daughter, Willa Goodfellow ’75, had gone to Reed, and the family spotted in Irena that unique hunger for learning that defines all Reedies. They encouraged her to apply.

“It was the first time in my life,” Irena recalls of arriving at Reed, “that I didn’t have to hide the fact I actually did some reading.” She majored in math and has fond memories of Math 200 with Prof. Hugh Chrestenson [math 1957–90]—also her thesis advisor—and of the legendary Prof. Joe Roberts [math 1952–2014], who taught advanced topics in analysis as a problem-solving class. “Sometimes we were stuck on some problems for weeks,” she remembers cheerfully. “But true to form, he wouldn’t step to the blackboard and fill it in. He made us suffer!”

But her most eye-opening classes may have been American labor history and American intellectual history with Prof. Casey Blake [history 1984–87]. “Growing up in Yugoslavia, it was all memorization and ideology. So this was the first time I’d seen that the study of history isn’t just memorization, but discovery, and that it can change societies.”

Irena couldn’t have gone to Reed without financial aid—“my parents couldn’t afford anything,” she says—and had to support herself. She spent one summer working for Prof. Neal Nelson [math 1984–87], Reed’s first computer science professor. Her team built a network for the Apple Macintosh, which had just arrived on campus. It was on Nelson’s team that she got to know her future husband, Steve Swanson ’84.

After graduation, she went to Purdue to get a PhD and taught at New Mexico State University before coming back to teach at Reed. She has written or edited three books and almost 50 papers, most of them focused on commutative algebra, a branch of abstract algebra that deals with mathematical objects that produce the same result when multiplied in any order. For example, you can put on your belt and then your watch, or your watch and then your belt—either way you get the same result. (That’s commutative.) But if you put on your shoes and then your socks, you get a different result than if you reverse the order. (That’s noncommutative.)

After her eureka moment with the checkerboard quilt, Swanson spent countless hours refining the technique. For several years, she believed that she was the first to discover it. Then last year, she stumbled across an obscure book published in 2003 by Rita Hutchens that outlines the same idea, albeit without the rigorous trigonometry Swanson employs.

Tube piecing isn’t her only quilting innovation. In 2011, she authored a chapter in the book Crafting by Concepts laying out the math behind semiregular tessellations—repeating patterns of more than one regular polygon—and giving a unique, characteristically efficient method for reproducing them in fabric.

Swanson is working on a book about tube piecing, a 435-page behemoth that forced her to get a new laptop because it kept crashing her old computer. As we scroll through it, I ask if she’s worried if some of her fellow quilters will be intimidated by the math. “I do, yes,” she admits. “I’ve had to simplify and hide some of it.”

But little by little, the idea is catching on. Local quilters rave about it. “The method isn’t just accurate and fast. It’s also pretty much foolproof,” says Jolene Knight of the Northwest Quilters Guild. “I think it’s just a matter of people understanding it. Once they get it, they’re going to be all over it.”

Foolproof or not, there’s undeniably a spark of brilliance behind the technique. It’s the same spark that spelled doom for her chess opponents, and that makes her such an inspiring teacher—that unpredictable combination of logic and creativity, order and chaos.