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WHEN KNITTING MEETS MATH: THE MOEBIUS CONSTRUCTION

Cover photo: © Jennifer Steingass


Knitting and math are closely linked. Whether it’s using your gauge to determine what size garment to knit, fitting pattern repeats into a given number of stitches, or using an “any size, any gauge” pattern – math is everywhere.


Most of the time, combining knitting and math is inevitable, and you don’t even notice it’s there. But sometimes, it's 100% intentional.


Enter the Moebius. What we call a Moebius is actually called a “Moebius strip” (sometimes a Moebius loop or Moebius band). It’s a mathematical surface with no distinguishable inside or outside, top or bottom.


In its simplest form, it’s a strip of paper (or fabric) put together on the short ends with a half twist to form a loop.


A woman holds a stranded knitting Moebius cowl with chevrons.
© Jennifer Steingass

The Moebius got its name from two scientists who “discovered” the loop in 1858, but Moebius loops can be seen in ancient Roman mosaics.


How does this mathematical surface influence knitting? Well, I’m glad you asked! The Moebius is the perfect form/shape to create a cowl. There are two main methods to create a Moebius while knitting.


  1. You knit a flat piece and seam the short ends of your strip together, incorporating a half twist of one of the ends.

  2. You use a special cast-on and actually knit in the Moebius form from the get-go. The second option is a well-known method, and once you’ve got the hang of the cast-on, you’re good to go. The number of patterns you can use is endless. Anything goes with a Moebius. Cables, lace, double knitting,… you name it.


To understand how the cast-on works, watch this video by Cat Bordhi.



Moebius patterns

To start you off, here are a few pattern suggestions. If you're new to Moebius, we recommend Meret Bützberger's Mrs Santa's Cowl. If you're familiar with brioche knitting, you can also try Briöbius by Carissa Browning.


on the left, a woman wears a red, green and white moebius cowl; on the left, a mannequin wears a green, grey and dark blue moebius cowl
© Meret Bützberger | © Carissa Browning

You can also try knitting seamed Moebius variations in stranded knitting, such as Jennifer Steingass' Recollect Cowl and Kate Davies’ Funchal Moebius.


on the left, woman wears a colorful chevron straded knitting moebius cowl; on the right, a woman wears a pink and grey stranded knitting moebius cowl
© Jennifer Steingass | © Kate Davies

Apart from cowls, the Moebius is sometimes used for handles on bags (especially if they will be felted) or even the neckline of sweaters.


Don't be afraid to experiment with Moebius knitting!

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