Knitting Around the Möbius

The mysterious Möbius Strip, or Loop, was discovered independently and almost simultaneously by two German mathematicians, August Ferdinand Möbius and Johann Benedict Listing, in 1858. It is a band or strip with only one edge and only one surface, and has been called the Riddle of the Universe.

You can prove this to yourself by cutting a one- to two-inch strip of paper about 10 to 12 inches long; twist one end 180 degrees—that is, just flip it over—and tape it to the beginning. Now, with a pen, draw a line down the center of the strip; keep turning the paper but try never to remove the pen from the surface. Keep drawing and turning and voilà! You will meet yourself at the beginning! But your pen never left the paper. It has traveled on only one surface.

To double-prove it, you can draw your line around one of the outer edges of the strip, again, never lifting your pen from the paper. Eventually you will meet your beginning; the band has only one edge. You may recall M.C. Escher’s drawing of ants climbing around a Möbius strip.

I remember when my mother, Elizabeth Zimmermann, was first made aware of this magic band. I had accompanied her to a workshop she gave for the Minneapolis Knitter’s Guild in 1982, and one of the students floored us all with a demonstration of the Möbius miracle using a strip of paper.

EZ’s brain immediately went into gear and, as far as we know, she was the first ever to knit a Möbius strip, which she dubbed the Möbius Ring,¹ using the paper-strip concept, i.e. a long, narrow, flat piece of garter-stitch, turned over at the end and invisibly woven to the beginning. In this mode, The Riddle of the Universe may even become a beginning knitter’s very first project (perhaps with help for provisional cast-on and weaving).²

Elizabeth Zimmermann’s drawing of a Möbius scarf from the book, Knitting Around; schoolhousepress.com publisher.

We began to knit an abundance of these fascinating scarves in single-strand unspun Icelandic wool—called Plötulopi in the yarn trade (which weighs nothing and, being unspun, is super warm, as the guard hairs are allowed to form an insulating halo around the finished fabric). We experimented with different lengths, and textures, plus many alternate ways to wear them.

The first time I added EZ’s Applied I-cord border to a finished scarf—even though I knew about the magic property—I was mentally preparing to finish one edge with I-cord, then apply cord to the other edge. As I worked along in that slightly hypnotic haze that a knitter is likely to drop into during a small, repetitive project, I inadvertently gave a startled jump when I finally bumped into the first I-cord. But but but . . . both edges were I-corded, yet I had never stopped working—because there is only one edge. Wonderful.

Full Möbius instructions are in chapter four of the newly updated edition of Elizabeth Zimmermann’s fourth book, Knitting Around. There are scarves in various textures, plus my son Cully’s design for both his old and new ideas for a Möbius Vest, and my Lace Möbius Vest. In his review of the updated edition of Knitting Around, Franklin Habit wrote, “And I think there will be little debate when I suggest that the chapter ‘The Knitted Möbius’ is one of the most influential pieces of writing on knitting ever published.”

Left: A Fair Isle yoke sweater graces the cover of the updated version of Knitting Around by Elizabeth Zimmermann; image courtesy of Meg Swansen, schoolhousepress.com publisher. Right: The original version was published in 1989; photo of original edition courtesy of Pamela K. Schultz

Besides the Möbius Ring, Knitting Around also contains scores of EZ’s other designs for sweaters, socks, mittens, shawls, coats, jackets, and many more garments. At the end of each chapter is an installment of her Autobiographical Digressions, plus plenty of drawings and paintings from her days at the Art Academy in Munich.

Notes

1. Do not be misled. Many of us have cast on a circular sweater or cap, and inadvertently twisted it before joining end to beginning. We first thought: O! wonderful—we can give instructions that read, “Join, being careful to twist!” Alas, that twist is 360 degrees, and the magic circle needs only a 180-degree twist.
2. In 2001, Cat Bordhi published a pattern for an ingenious way to cast on provisionally for a Möbius scarf, using the cable section of a 40" circular needle as her auxiliary wool. The twist is established in the doubled-circle of the needle, and you knit two (half) circles for each complete round. Cat’s scarf is knitted from the center of the strip to the outer edges. Isn’t knitting amazing?

Meg Swansen, the daughter of Elizabeth Zimmermann, has become one of the most influential and best-loved figures in the knitting world, introducing many knitters to the traditions of Latvia, Armenia, Estonia, Iceland, and the Scandinavian countries. An internationally known designer, author, and teacher, Meg is also the owner of Schoolhouse Press.