# Math Knitting Concepts & Examples

## Math and Knitting: My Story

This is a story about how a proud non-math user, who would have sworn she had no use for algebra, had an eye-opening encounter with upper-level math in the real world through knitting and lived to brag about it.

When I was homeschooling my twins and we were learning about skip counting (covered in the *Primer* through *Gamma* levels of Math-U-See), I mentioned to the kids that, as a knitter, I use skip counting all the time on every project. As an experienced and fairly advanced knitter, it’s not unheard of for me to have 400+ stitches on my needles if I’m using a very fine-gauge yarn. I don’t want to count 400+ stitches by ones. But it’s critical to start with the proper number of stitches, so I skip count my cast-on stitches, usually by twos, and then skip count again (and sometimes again!) before I start so I’m starting with the proper number. There’s nothing more discouraging than realizing six rows in that you have 398 stitches when the pattern calls for 400.

Then, during another lesson in *Delta*, I thought about how more advanced patterns don’t say, “Knit 4, increase 1 stitch.” Most of my patterns will simply say, “Increase X stitches evenly across the row.” Boom! Division in action! I have to take the total number of stitches currently on my needles and divide by the number of stitches to increase; this tells me how frequently I need to add a stitch to end up with the new total at the end of the row.

So that got me thinking about all the ways that I adjust and adapt patterns for all the different projects I knit on a regular basis, and I wondered: could this be…math? I talked to our Curriculum Development folks, and they assured me that, yes, it certainly is math, and not only that, I am actually using geometry, or even algebra, on a regular basis and don’t even know it.

## Ways I’m Using Math While Knitting

Besides the arithmetic I’ve already identified, here are some other ways I (apparently!) use higher math functions:

### Ratios in Knitting

Like most knitters and fiber enthusiasts, I don’t always purchase the yarn called for in the pattern as written. Perhaps it’s a fiber I don’t like, or more likely, I have something in my stash of lovely yarns that I think would be perfect for the project. Yarn comes in various weights, and if you want to have a project fit the way it is designed, you need to make sure that your knitting matches the gauge recommended in the pattern. Alternately, if you’re brave and a little daring, you can adapt the pattern to suit the gauge of your preferred yarn. This requires an understanding of ratios. If you are knitting the front of a sweater and the pattern calls for 90 stitches to make a piece 18” wide, you can determine that you have a ratio of 5 stitches to 1 inch. If your selected yarn gives you a gauge of 7 stitches per inch, you’ll need to cast on 126 stitches to end up with a piece the same width– or, if you get 4 stitches per inch, you’ll only need 72 stitches. This means that I’m using ratios and proportions to make sure my gorgeous baby alpaca/cashmere blend results in a sweater that fits.

### Congruence

I’m an avid sock knitter. I love the colors and the fun yarns and tailor-fitting the sock to my feet and the portability of a small project and everything about knitting socks, so I’ve made a lot of them. My process is, I’ll keep a loose eye on the pattern for the first sock, measure and try on a lot, and make sure that the first sock is pretty much exactly how I want it. Having fairly normal feet, in that they’re nearly identical in size and shape, for the second sock I ignore the measuring and trying on and just knit it. I used to think that I just wanted the second sock to match the first. But now that I’m a “math person,” I know that I want it to be congruent – to be identical in every way to the first one!

### Slope

I’m currently knitting a V-neck cardigan, using a pattern intended for experienced knitters. The instructions are given fairly clearly (to those well-versed in knitting pattern language, that is) for the right front side. The left front? The complete instructions are: “Knit as right front, reversing pattern and shaping.” Well. That would be a bit of a kick in the head…if I didn’t know that this was a reflection (a type of transformation)! And to make the V-neck, I (apparently) was finding the slope of a line. This allowed me to determine how frequently I needed to decrease and in which direction to achieve the slanted edge of the V. After performing these bits of math magic, I ended up with the following.

### Dilation

Let’s say we make ourselves a sweater and it’s so adorable that we want to make one for the WHOLE FAMILY! Obviously we need to make the pattern larger or smaller. To do that, we perform another transformation – dilation. (Note: it’s possible for this to get out of hand.)

When I could finally put down the pencil, as it were, having finished school, I thought I was finished with math forever. When I picked up my knitting needles, though, I found that math mattered more than ever.

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