This page includes plain text instructions for the Mobius Scarf, a Klein Bottle, and a Klein Bottle Hat. It’s been on the Web since at least 1994. I’m not sure who devised the patterns.

Possibly a derivative of Elizabeth Zimmermann’s Moebius Ring, which first appeared in an issue of her 1-page newsletter Wool Gathering and was also reprinted in Vogue Knitting Holiday 1987.

from the Wool Works copy:

It’s a scarf that’s a mobius strip. One edge, one side, and basically a loop with half a twist in it. Hmmmm… the Knitters magazine on the Luxurious Knits had two recipes for the scarves in it… You can take a piece of paper, put a half twist in it, and join the ends and you’ll see that the resulting thing has only one surface (that you can follow around twice) and one edge (that goes around the object twice).

The other is harder to explain with textual means, but, basically, the idea is to knit the scarf along it’s one edge (and, no, it’s not like knitting a circle but with the row twisted, that will give you a full twist, not a half-twist).

The advantages to a mobius strip scarf are

1. if you put it over your neck and it’s straight along your neck, the half-twist folds flat under your jacket;
2. being a loop, the scarf never falls off; and
3. if your ears are cold and you’ve made it long enough, you can lift the “fold” give it a half twist and have a ready-made, comfortable hood with extra protection at your throat.