Knit One, Purr Too

A little math lesson

I would like to show you one of the projects I am working on right now.

I fell in love with this yarn last year, during my great summer of afghans, and ordered enough to make myself an afghan. What with all the other gift knitting I've been doing lately, I didn't get around to it til now. And like nearly every other afghan I've made, I couldn't find an existing pattern that really spoke to me, so I started swatching.

First I swatched one lace leaf pattern I found online, and while I really liked it, the combination of all those purls and decreases meant that I'd likely not have enough yarn to make a full size afghan (the unfortunate thing about lace patterns in acrylic is that you cannot count on blocking to smooth things out later). I moved on to a second lace leaf pattern, but had a similar lack of success.

Then I got the bright idea to do this diagonal basketweave. It is really quite simple. You start with one corner, which is one square (I'm doing 4 stitches per square) and then after you make the square, you cast on an additional square's worth of stitches on each side, and swap knits to purls and purls to knits, and on and on you go. My first swatch with this idea I quickly discovered how important it is that your squares be actually square (corners on rectangular afghans are supposed to be 90 degrees, for some funny reason). Then once I'd narrowed down an actual guage (4 stitches across, 6 rows down = a 1 inch square) I decided that I would like it a lot better if I started the corner on a point. If you have been keeping count here, that is 5 different starts for this afghan, and actually there were a total of 6 because I ripped it out one last time to rework the starting point.

But anyway. The whole point of telling you about this particular afghan-in-progress is that when I started pondering how wide I wanted the afghan to be, it got me thinking. Knitting is, after all, just math with a little yarn thrown in. However, how often do you actually get to do anything more exciting than addition or multiplication these days, hmm?

You see where I am going with this?

Because I am using (mostly) perfect squares, both sides of my triangle should be exactly the same length, and the corner between them should be a perfect right angle, which means that I am knitting myself a very large isoceles triangle. I know my stitch guage, because each of the squares I am using is 4 stitches for one inch, and I know the length of the diagonal edge, because that's the one I am working on, and I always know exacty how many one-inch squares I've got on the needles.

So when calculating out how much futher I need to go before I don't have to increase anymore, I could do it one of two ways. I could do a few pattern repeats, then lay it on the floor and measure it obsessively. Or I could whip out my handy dandy calculator and, based solely on the fact that I know the width I *want* it to be, calculate out how many stitches (or squares) across I have to do before it's going to be wide enough. And I can do this because way back in the dusty recesses of my brain, I remember grade school math, and more importantly, I remember the Pythagorean Theorem, which states that the square of the diagonal is equal to the sum of the square of both sides in an isoceles triangle. Based on this calculation (and knowing that because of the pattern I am using I will always have an odd number of pattern squares), if I want my afghan to be 40 inches across, that means I have to have....

Well, I won't spoil it for you. Surely there are other closet math nerds out there who find this sort of thing just as exciting as I do. Right? Yes? Tell me I am not the only one who finds unreasonable glee in discovering new ways to apply geometric equations to real life?

Posted by Jenipurr at January 17, 2006 01:32 PM