Tag Archives: math for crafts

Suggestions for doing math as it relates to handcrafts.

Asymmetry or Symmetry?

(This is part of a series of posts on different ways of hiding meaning in your knitting.)

Table of Contents: Embedding meaning in Your Knitting | Converting Words to Numbers | Making a grid | Asymmetry or Symmetry? | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Addendum: Ribbing | Further Resources

You might be perfectly satisfied with the grid you have without any further modification. If so, you’ll want to skip to “Converting grids into stitch patterns”.

The first step in deciding this is to lay out multiple repeats of your stitch pattern to see if you like it as an all over design (if that’s what you’re after, of course).

If I take the base 6 version of peace from “Making a Grid”

Peace charted on a 6x10 grid

and repeat it three times in each direction, I can get a sense of how the repeats interact at the edges:

Peace charted on a 6x10 grid and repeated 9 times

This has distinct possibilities as it is, but let’s see what happens if I play with it some.

The first obvious variation is to mirror it. Here it is mirrored horizontally:

Or if you don’t like the doubled squares at the edges, you can overlap them:

Here is the latter, in a three by three repeat:

Now mirror it in both directions:

and see how it looks repeated, this time three times horizontally by two vertically (because the symmetry makes it easier to see how the repeats interact).

If the grid has more white space than you like and you’re not making a secret code, you can mirror the grid on itself so that it’s doubled (shown in two colors to make the mirroring clearer):

If you have an even number of squares, you can again eliminate duplicate columns if you’d like:

And here is the allover layout of the latter:

These are probably enough ideas to be going on with, but if you’d like to try out some other variations (whether with the original asymmetrical grid or the mirrored), have a look at the pattern design resources in Further Resources.

Just for an example, one basic pattern repeat variation you’ll find is the half drop, asymmetrical:

and symmetrical:

Next post: Converting grids into stitch patterns.

figuring the percentage of a circle that’s been made

Okay, say you’re knitting a doily from the center outward and you know how many rounds the whole doily is. It turns out that that there’s a fairly straightforward way to calculate when you’re halfway done (or whatever). You can’t just say “I’ve knit 30 rounds out of 60, I’m halfway done”, because the number of stitches per round keeps growing.

Here’s the easy math: take the number of rounds you’ve knit so far and square that number (multiply it by itself). Take the number of rounds you’re going to knit and square that. Divide the former by the latter, and that’s the percentage.

30 rounds out of 60 means

(30 x 30)/(60 x 60) = 900/3600 = 25% or a quarter done.

There’s more detailed math below, but here’s a good rule of thumb:

Approximately half the yarn will be used when about 70% of the rows have been knit. It turns out that this works for any geometric shape where the knitting starts at a point and increases at an even rate.

(I don’t know that this works for pi shawls.)

Continue reading figuring the percentage of a circle that’s been made