Upon studying the instructions for vintage Vogue Pattern # 1071 (View A) last night, I was perplexed by the instructions for creating a long bias strip to use for binding the neckline. The pattern piece looks like this:
With right sides together, pin ends of CONTINUOUS BIAS together, matching symbols. Stitch. NOTE: Edges will not be even at ends of seam. Starting at one extending end, cut along cutting line, forming one continuous bias strip, as shown.
As shown? As shown??? The illustration provided in the instructions was worse than useless. All I could do was cut out the fabric, play around with it, and see what I could come up with. I was delighted, upon fitting the two ends of the pieces together in the only way that would possibly produce one long continuous strip of fabric, to find that I had constructed a Möbius Strip, which is a strip of paper (or fabric, in this case) with the ends of the strip fastened together after giving the strip a 1/2 twist. The resulting strip has only one boundary, which you can prove be drawing a line along the length of the strip starting at the seam. The line will end up at the seam, but on the "other side" of the strip. Here's the way the fabric looks: