Is there a topologist in the house?

Seriously. Because I would really like to know what is the proper name for this form:

It's a double-knit moebius. But what's the mathematical name of this thing? It's got a half-twist, so it must be a moebius. But it has an inside and an outside, which means it has volume, so it can't be a moebius. So what is it? (My best guess: some kind of twisted toroidal form). If there are any topologists out there reading this, I hope you know the answer, and that you will let me know.

Here is my latest video, which explores these topics.

(View in YouTube).

Here's where this saga began...

Once upon a time I learned from Cat Bordhi's book A Treasury of Magical Knitting how to knit a moebius. Pretty cool. Then I heard through the grapevine that Judy Becker had made a doubleknit moebius, which naturally made me want to try to make my own. Only I wanted mine to be continuous, with no insertion point. The image above is what I came up with. The red crochet chain shows where the stitches came off the needles.

While I was knitting it, I was vastly curious what I would end up with if I bound off the edges separately and unfurled it, instead of grafting the edges together. So, here's what you get if you pull off the crochet chain...

Pull the sides apart...

Untwist, and voilá!

To my complete surprise, I found it to be the *exact same* form that you get if you cut an ordinary moebius down its center axis: a tube with 720 degrees (2 full turns) of twist.

Ergo, you can take this form and re-shape it into an ordinary moebius (note how the knit and the purl sides meet in the middle here):

I don't know about you but I thought, oh man, this is way cool!!

If you stuff the closed form to give it some volume, you get this:

Note how the half-twist goes away as it gains volume, and instead you get a spiral running through the middle. Awesome!




I've continued to explore this topic and found that there are yet more ways to create a doubleknit moebius, some of which may surprise you. Stay tuned...

Jeny's Stretchy Slipknot Cast-On

Since Jeny's Surprisingly Stretchy Bind-Off was published in Knitty earlier this month, a number of knitters have asked me if there is an accompanying stretchy cast-on. Well, there is. It is the most elastic cast-on I know -- more elastic than the classic long-tail cast-on. And this one is not a long-tail cast-on so you don't have to worry about how much yarn to leave for the tail.

Like my bind-off, this cast-on is super-stretchy:

And like my bind-off, this cast-on also hinges at the bends of the ribbing.

I've created a video to show you how to do it.

This video is also available on YouTube at http://www.youtube.com/watch?v=3n8E3I6Cg2k.

The basic premise of this cast-on is this:

1. Make a slip knot.
2. Make another slip knot.
3. Continue.

It's really as simple as that. But it's a little tricky getting the slip knots to all line up right next to each other on the needle. The video will walk you through the tricky parts.

The origin of this bindoff is somewhat of a mystery. Years and years ago I learned it, or something like it, from a book. I later forgot how to do it, and couldn't find the original resource I learned from, or any knitters who knew it, so I had to figure it out all over again by myself. This happened a few more times over the years. And I still can't find the resource, or any other knitter who uses this cast-on. So who knows if it's an original, or if it's some ancient cast-on, lost in the midst of time. It doesn't matter -- it's an awesome cast-on that every knitter should know about. If you've ever used or seen anything like it, please post a comment!

Warning: This cast-on is a bit finicky about the kind of yarn you use. You should use yarn that is a smooth texture and uniform in width. Trying to do this cast-on with yarns like chenille, or any of the yarns shown here, will give you nightmares!

ADDENDUM 9/28: Now that this post has been up for a few days, other knitters who know this cast-on (or very similar) are coming out of the woodwork. Yaaay, I knew you were out there!

Check out this video: http://www.youtube.com/watch?v=DKwYH-vqJL0

The author twists the yarn around the needles with a different set of motions, but the end result is, in fact, the same.

ADDENDUM #2, 10/4: A-HA! Confirmation that yes this does in fact exist in print. See Montse Stanley's Buttonhole Cast-On, p. 76, fig 2.37.