Knitting the non-Euclidean way

[Warning: This post contains high levels of knitting geekery. Please be advised. —The Management]

The first sweater I ever knitted was made in pieces: a front bit, a back bit, two sleeves (each made flat and seamed into a tube), and a couple of bands that went on the bottom of the front and back bits and the bottoms of the sleeves. Like a lot of sweaters, it required assembly once I'd made the pieces: a seam up each side, followed by the laborious process of setting in the sleeves and stitching them to the body. That sweater, despite the loveliness of the yarn, is still hibernating among my almost-finished-but-not-quite projects; someday, I'll probably give in to the inevitable, unravel the whole thing, and use the yarn for something else that doesn't trigger my hatred of sewing.

My second sweater was a great improvement: a cardigan made all in one piece (a rectangle with some shaping around the shoulders and neckline, and sleeves picked up at the armhole). That one I actually finished and still wear. I made my third sweater entirely in the round, using Elizabeth Zimmermann's method, which makes for a splendidly simple design: the sweater is a tube, the sleeves are two smaller tubes that attach to the body once you've set aside some stitches for the armholes, and you just narrow it down as you get closer to the top.

My next sweater, like sweater #2, is a seamless cardigan, but this one is more conceptually challenging. After I downloaded the pattern, I couldn't quite wrap my head around it. There's an extra drapey section that extends the front of the sweater and attaches to the back of the neck to form a shawl collar, and I had a hard time picturing what happened up around the shoulders. There's a diagram in the pattern, but what I really wanted was a 3D visualization.

I consulted the more experienced knitters in one of my knitting groups, and one of them (thanks, Ruth!) suggested making a model out of paper or fabric. So I did, and it worked; I now have a clear idea of where I'm going:

Paper model for a sweater

It's hard to tell from the photo, but that's a 3/4 view of the sweater model, minus sleeves, and with the drapey part fanned out in front, except it's paper so it doesn't actually drape the way the finished product will.

I was delighted to find that not only did the model help me visualize the sweater in three dimensions, it also reminded me of one of those obvious but sometimes forgettable truths about knitting: knitted fabrics don't have to be flat. Paper is flat. Woven fabrics are flat. If you want to make something fitted and complicated and three-dimensional out of, say, a bolt of cotton, you have to cut it carefully into pieces of the right shape and size and sew it (or gather it, or iron it into pleats, or starch it into ruffles, but I digress). But if you're knitting, you don't necessarily have to make things in pieces and sew them together; you can just keep going, increasing here, decreasing there, warping the plane with short rows, breaking out into spirals and curlicues. You can make tubes, and sock heels, and bobbles, and Moebius strips, and hyperbolic surfaces. If I were slightly more of a math geek I'd be going off about non-Euclidean geometry* right about now, but instead I'll just refer you to the staggeringly brilliant Crochet Coral Reef project and its accompanying pages on hyperbolic space.

After the geeky spatial puzzle-solving challenge of working out how a sweater like this fits together, not having to sew seams at the end is gravy—though it'll probably make the difference between a sweater I may actually wear on my travels this summer and a sweater that languishes perpetually unfinished.

* Not that there aren't risks to making non-Euclidean garments. Eldritch,
, uncanny risks.

5 Responses to “Knitting the non-Euclidean way”

  1. Jill Smith says:

    Lovely – it does a lot of the same things (functionally) as those cardis that have long tails in the fronts, but much more attractively.
    For sheer brain-bendery, I also love EZ’s baby surprise jacket.
    Oddly enough, though I hate hand-sewing, I like finishing. Weird, no?

  2. Johanna says:

    I’ve yet to make my first sweater, but when I do, there will NOT be lots of seaming to do.

  3. Amanda says:

    I highly recommend the basic sweater-in-the-round method in Knitting Without Tears: the only fiddly bits for me were figuring out where the sleeves should go and finishing off the collar.
    I haven’t made the Baby Surprise yet, but it certainly looks like fun!

  4. Laura says:

    Being self-taught mainly from historical documents or existing old garments or both, I just assume that your basic sweater* casts on at the bottom, knits up to the chest, then you leave the stitches for the front and back on a holder and knit a sleeve down to the cuff and cast off, repeat for other sleeve**. Then you take your waiting stitches for front/back and knit your way up, picking up from the sleeve-top and decreasing for shaping to the neck, knit your neck-edge and cast off. Done. No sewing.
    *is this the right garment? I mean a thing you pull on over your head, not one that buttons up the front. If you all mean what in Britain is called a cardigan, that buttons up the front, then just ignore me or use steeks 🙂
    ** cunning because then when the elbows wear out, you just unravel to above the elbow and re-knit a new length of sleeve. Much more sensible than knitting from the cuff up.

  5. LieYu says:

    “I consulted the more experienced knitters in one of my knitting groups, and one of them (thanks, Ruth!) suggested making a model out of paper or fabric. So I did, and it worked; I now have a clear idea of where I’m going” it seem that you like the Ruth made,.. thanks for share the story about it,.