Knitting Math

Yesterday I posted about ambitious knitting. Which got me thinking about why I knit. If you enjoy a craft, it’s usually because you enjoy both the act of doing it as well as the finished product when you’re done. Many knitters are perfectly happy knitting and wearing garter stitch scarves. There’s clearly no obligation to pursue ambitious knitting projects, so why do I?

For one thing, I like wearing socks and sweaters and lace shawls, so it makes sense that I’d want to make those sorts of things. And for another… well, I suppose I view knitting as an intellectual exercise as much as a craft. I’ve always loved puzzles and logic problems. Heck, most of my undergraduate & graduate studies were spent problem-solving (mathematics, operations research, and computer science). B.C. (before children), I designed computer software and websites. I guess knitting was a logical progression!

Knitting presents an interesting puzzle for me… how do you manipulate yarn to make complex lace patterns or to fit the curves of a human body? The mathematician in me loves problems like that. And the knitter in me appreciates that knitted fabric is nice and stretchy, so dipping into triple integral calculus is purely optional.

I always have to stifle a chuckle when I hear knitters complain about “knitting math.” To me, that’s some of the fun of it! Yes, I do realize that this is not a common view. 🙂

Case in point: My Lanesplitter Skirt. The original pattern calls for casting on in a corner, increasing on both edges to make a large triangle. When the right side is the length you want the skirt to be, you start decreasing on the right side and continue increasing on the left side. When the left side is as wide as you want the skirt to be, you decrease on both sides back to a point, then seam up the short side to form a tube. Very clever pattern.

Before I decided to make one of my own, I spent some time reading the project pages on Ravelry (okay, not all 1,457 of them, but enough of them to get an idea about the pattern). Many people commented that they didn’t like the way the stripe colors didn’t match up at the seam, so they suggested that you start with a provisional cast-on, work only the straight section (decreasing at the start of every right-side row and increasing at the end), and then graft the skirt closed at the end, so you get a seamless tube. This sounded brilliant to me!

But how to determine the correct size? I reasoned that we’re knitting a parallelogram (the top and bottom of the skirt will be the same number of rows and thus should be the same size once blocked, and the sides of the seam to be grafted will be the same length). The original pattern called for increasing equally on both sides of the work, so you should end up with a triangle with roughly equal-length sides. This means that you have a 45-45-90-degree triangle. (Sorry if that flashback to geometry class was painful for you!) Which means that the hypotenuse of the triangle is the length of one side times the square root of two (approximately 1.414). So if I want my finished skirt to be 19.5″ long, I need to cast on enough stitches to make approximately 27.6″ of knitting (19.5 times 1.414). My gauge (after washing) was 19.5 stitches per 4 inches, so I needed to cast on 27.6″ times 19.5 stitches divided by 4″ = 134 stitches. I expected the weight of the fabric to cause the fabric of the finished skirt to stretch a bit more than my gauge swatch, so I rounded down to 130 stitches.

I just measured my skirt again, and found that it’s about 18.5″ from one edge to the other. It hasn’t been blocked yet, so with blocking and the way I anticipate that the fabric will stretch lengthwise when I wear it, my skirt should come in right about 19.5″ when it’s done. Yay for knitting math!

How do you feel about knitting math? Do you embrace it or avoid it?

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