Infinity scarves and Moebius scarves are both popular with knitters, although many people I talk to are unclear on what they really are. It's based on the Moebius strip, which is a mind-bending bit of topographical magic.
Cut out a long thin strip of paper. Give it a half twist (flip one end over) and then tape the two ends together. Now here's the magic: take a pen and start drawing a line on one side. Your pen will follow the strip of paper all the way around to the taped join - where you will find you are suddenly on the other side. Your pen will make two "laps" of the paper before it meets its own track again.
This is a lot easier to explain in person than in writing. Here's a video that demonstrates how it works.
Aside from being a very spiffy party trick, and a fun thing for kids to play with, an infinity scarf has another special property: it lies completely flat.
If you just seam together the ends of a scarf in a regular loop and wear it around your neck, you will have to fold the scarf at some point to get it to lie flat. It will tend to loop up at the bottom, like a cowl neck on a sweater.
However, because of its weird geometry, an infinity scarf naturally lies perfectly around your neck. (It reminds me a big of the recycle symbol.)
There are two ways to make a Moebius scarf: you can knit a regular scarf, give it a half twist, and seam the ends together. Or you can try Cat Bordhi's impressively brilliant Moebius scarf cast on. The Bordhi method is a little more difficult to master, but it results in knitting a Moebius scarf from the inside out, in two directions at once, which is pretty entertaining in and of itself.
Image courtesy Flickr/Aine D
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