Now we explore a different kind of strip, in which the yarn travels parallel to the boundary. We call such strips helical because the yarn travels in a helical pattern around the strip in an ever-widening path (Figure 4).
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The interested knitter can follow the instructions in the appendix to make a helical strip. A strength of this method is that it only involves knitting; no sewing is necessary in construction. The process is also more interesting than the transverse method because the piece develops as a mobius strip from the start, whereas a transverse strip is only a simple rectangle until the final step.
The helical strip shown in Figure 4 was made with plain stockinette. The pattern of stitches has a very obvious seam, which appears in the figure running horizontally across the middle of the diagram. We use the word ``seam'' to refer to a line for which the pattern of stitches on one side is not a smooth continuation of the pattern on the other side.
The seam in Figure 4 is inevitable because stockinette does not possess front-back symmetry. However, recall that ribbing and garter do have front-back symmetry, so seamless transverse strips can be made from these patterns. At first, they appear also to be useful in making seamless helical strips. However, more subtle difficulties arise.
A ribbing helical strip also has an obvious seam at the center line. This is inevitable because ribbing is the same on both sides only when flipped left-to-right, not top-to-bottom (Figure 5), making it suitable for seamless transverse strips, but not for seamless helical strips. More precisely, a seamless transverse strip can only be made from a pattern that has rotational symmetry about a vertical axis and a seamless helical strip can only be made from a stitch that has rotational symmetry about a horizontal axis.
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Garter stitch has both of these symmetries, but a garter helical strip (Figure 6) has a short transverse seam, which appears in Figure 6 along the vertical line running from the center of the diagram to the top. The pattern to the left of the seam does not align with the pattern on the right. This stems from the fact that garter is a two-row pattern; only every other row repeats. This is a problem in helical knitting because each row is a smooth continuation of the previous row. To produce garter, one must switch between knitting and purling after each cycle around the strip, and these switching points form the seam.
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We can avoid this difficulty by using a double helix made from two separate yarns (Figure 7). One yarn is always knitted and the other always purled so that the switching problem does not arise.
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We managed to produce a one-yarn seamless helical garter strip by starting in the middle of a yarn and working towards both ends (Figure 8). This strip is very similar to the one described in the previous paragraph except that it consists of a single piece of yarn. Starting in the middle of a yarn is a technique rarely used by knitters, but it satisfies the criteria of pure knittability because the strip can be made without relying on the ends of the yarn.
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In all the helical strip diagrams, one can see an area of irregularity around the center point, where there is one more row to the right than to the left, causing the stitches to the left to take a distorted elongated shape. In the double-helix strips, the effect is heightened because there are two extra rows. Because these irregularities are confined to the area around a point rather than a whole line, we do not consider them as troublesome as seams.