Knitting a moebius shawl or scarf is a fun way to create wearable math. And a great way to keep the kids busy in the waiting room of the doctor or dentist, trying to decide which is the inside and which is the outside!
Patterns for these abound in books and on-line. As a rule of thumb, I use a Size 15US, 35" circular needle, and cast on about 80 stitches (which works out to 160 once you've done the pick-up for the moebius -- see instructional links below). Be sure to use a loose cast on and a loose cast-off! Size of yarn doesn't matter -- a thick yarn gives a cushy moebius, a thin yarn gives a lacy moebius. Pull out your crazy yarn and add some pizzazz!
There are several ways to knit a moebius, from dirt simple to "in the moebius". Planet Shoup has a great set of instructions of each of these ways:
http://www.planetshoup.com/easy/knit/scarfmb3.shtml
They include three different variants on how to make a moebius -- the "make a flat piece and twist it when joining" variant (the easiest); the "make a mini-moebius flat and then join, pickup and knit a true moebius" variant (a good "transition" moebius to actually knitting a moebius); and the "make a real moebius by picking up the cast-on edge" variant -- where you actually knit moebiusly! Very fascinating.
The last one is my favorite, I find it really fun to knit moebiusly, and prefer that cast-on to the Bordhi method, which involves wrapping two layers of needles.
The Cat Bordhi method, a 4th variant, was recently featured on DIY.
And if you want a crochet one, there's this:
http://home.comcast.net/~gandal195/MoebiusShawlPattern.htm
(based on a post by me on spindlers, 3/7/07)
Finally! found the DIY link for Cat Bordhi's, here: http://www.diynetwork.com/diy/na_other/article/0,2025,DIY_14142_4894528,00.html
What's your favorite thing to knit with a moebius base? besides the shawl/scarf/neck cowl, there are fun ways to use a moebius in a hat band, or as the handle of a felted basket. I've done shawls, hat bands, and baskets, and have a deeper felted tote bag planned next. But what shall I knit after that with the moebius? I'm open to suggestions!
