Sooooo, did you happen to notice that the blocked square wasn't exactly square? Yeah, me, too. :( And even though I blocked it really hard, it still wowed on the sides. Double :( :(.
Blocking the square as hard as I did had an additional downside. The fabric is way less dense than I intended, and the colourwork especially, looks all stretched out.
I thought for a while the problem might be the corner increases. I was doing Kf&b (Knit through both the front and back loops) of each end stitch. That's not a balanced increase, since each new stitch appears to the left of the original stitch. In my mind, these are 4 equilateral triangles (the 4 wedges that make up the squared-off circle). And they must be symmetric.
Instead of Kf&b, I tried to put a leaning decrease one stitch in from the edge of each side. I won't bother to describe it in any more detail here, because it didn't work. Oh, I like the symmetry of it, but the sides still wowed.
A little math seems to be required, and a little more thought.
For the final block to end up at 12 inches, the radius must be 6 inches. OK. Got that. The inner angle of the wedge must be 90°. I think with the blocking, we've got that. BUT the outside edge of the wedge (the perimeter of the square) should be 12 inches, too. I STRETCHED it to 12 inches with the hard blocking, but should blocking (like marriage) really be that hard? I don't think so.
And that's what brings us to the question of gauge. With Cascade 220 Superwash in my hot little hands, with 4.5 mm needles, I am getting a stitch gauge of 5.5 stitches/inch. So, for a 12 inch outside edge, I ought to have 66 stitches (for each wedge). And what do I have? Only 44.
I forgot about row gauge. I am getting 7 rows/in. That means to achieve 6 inches of knitting, I need to do 42 rows. If I started with 3 stitches, I need to increase 62 stitches over 44 rows. Or, more precisely, over 21 rows, since I increase on alternate rows. This is where my left brain moves over so my right brain can shout, "62 divided by 21 is VERY CLOSE to THREEEEE!"
And that, Knitting Touristas to the Kingdom, is what I'm going to try next. I will make 3 increases in alternate rows. A left leaning increase one stitch in from the starting point. A right leaning increase one stitch before the last stitch. AND, wait for it........one increase right dead centre in the square. It needs to be symmetrical though. Hmmmmm......
I don't think I can visualize this until I actually get the wool on my needles. Stay tuned.