Create Pi Shawl function (and also half-pi)

[terriko]

This is one of the shawl shapes mentioned in #11, but I'm describing it here in more detail so it's a more bite-sized issue.

A pi shawl is a circular shape with regular increases as the radius of the shawl grows:

https://www.craftsy.com/post/pi-shawl-patterns/

But pi shawls, while still worked from the center out, only require a few shaping rows in the entire project. Basically, every time you double your distance from the last increase round worked, you work another increase round. These infrequent increase rounds make pi shawls a great option for lace knitting.

It would be nice to have a function that, given a gauge swatch, could tell you how many rows to work between increase rows to get the desired flat circle, printed as a pattern or as a set of numbers, and maybe also have it calculate how many rounds you'd need to reach a desired size (given the gauge).

Similarly, a half-pi shawl is the same idea but only half the circle is worked. The math would be the same for how many rows to work but the instructions would be different. You'd probably want to make half-pi an option on the full-pi function.

[jinder1s]

Hi Terri, can you explain to me the mathematical relationship between a round gauge and the number of rounds before increases? As far as I can tell, the number of rounds before you do the 1st increase is arbitrary, lets say do the first increase after n rounds. All the increases after the 1st happen on the 2ni, where i represents which increase step you are on. So the 2nd increase would happen at: 2n2 rounds(where i=2), and the 3rd increase would happen at: 2n3 rounds(where i =3).

[terriko]

The first increase depends on how many stitches you cast on and your gauge, so it's not entirely arbitrary but there's also some flexibility (literally, as in the fabric stretches). I'd say that it's probably safe to assume that the first increase usually happens on row 2, and we can hard-code that in for now. That's because if you wait much longer than row 2, you wind up with a little puckered bit in the centre of your circle where the stitches haven't increased.

I did a quick search for a simple starter pattern you can look at and here's one: https://www.yumiyarns.com/single-post/pi-shawls-a-recipe-a-free-pattern

They're starting with 9 stitches (call this row 0, though knitters usually say "cast on row" rather than assigning a number. But I find 0 easier because I learned programming before I learned knitting), knitting one row (row 1), then doing the increase in row 2.

When we get to refining the equations later we could probably figure out some good math for number of stitches to cast on relative to gauge to get the piece to lie perfectly flat all the time and then add that, and maybe rethink if row 2 is the right choice for, say, half-pi shawls (which typically have a different start including an edging)