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Transverse Strips

The most straightforward way to knit a mobius strip is what we call the transverse method, in which the yarn follows a course back and forth across the strip (Figure 1). Each mobius strip diagram depicts a strip that has been cut and unfolded to form a flat rectangle.

Figure 1: A transverse mobius strip made from garter. Each mobius strip diagram depicts a strip that has been cut and unfolded to form a flat rectangle.
Transverse garter strip

Because a mobius strip has only one side, a homogeneous strip must necessarily use a pattern that appears the same on both sides. Basic stockinette (Figure 2) is unsuitable because it has two different sides. For reference, one side is called ``knitted'' and the other side is called ``purled''.

Figure 2: Stockinette is the most basic knitting pattern. The knitted side (left) and the purled side (right) of stockinette are different, making it unsuitable for seamless mobius strips.
Stockinette stitch

Both ribbing and garter (Figure 3) have front-back symmetry, and either can be used to make a homogeneous transverse strip.

Figure 3: Two simple patterns: Ribbing (left) is made from alternate columns of knit and purl stitches. Garter (right) is made from alternate rows of knit and purl stitches.
Ribbing and garter stitches

The interested knitter can follow the instructions in the appendix to produce a transverse strip. At the end of the construction, the knitter must graft the open loops of the first and last rows of stitches together. Grafting consists of using a large sewing needle to run the yarn through the two sets of loops so as to join them in an identical manner to the way every other row of yarn joins the rows above and below it. We consider this grafting to be a shortcoming of the method. Grafting differs fundamentally from pure knitting in that any knitted piece can be made while pulling yarn from an infinite ball, whereas grafting requires that the yarn be cut and the end worked through the fabric.


next up previous
Next: Helical Strips Up: vismath-paper Previous: Introduction