But that is okay, since I will never need to think again! Prompted by a comment from my ringneighbor, the esteemed laurie from Crazy Aunt Purl, (who is kind enough to read even though there is no personal information! Sorry! Not really worth the blogstalking effort!), I started hunting the internet for more clues about Elizabeth Zimmerman's Pi Shawl, which was the original inspiration for Wendy's Kitty Pi Bed. I confirmed that my original shaping was the same as EZ (work even double the previous number of rows, then increase in each stitch). I knew before I knit the original giganto Kitty Pi that the shaping was only approximate, and would get worse with size, but thought it would felt out okay. And in a relative sense, it was okay - it's only a cat bed! But the outer part was wrinkly (too abrupt a change at that size), and the decreases should have been spaced out farther - plus with the Noro, the striping changed drastically at that point.
But, I actually like math, so I was looking forward to making a nice formula for the kitty pi. Unfortunately for me, everything that is possible in knitting has already been done, and now people have blogs to communicate them... and doubly unfortunately for me, I'm pretty good at finding information on the internet. So, I present the already worked out formula, from Rudbeckia at Learning Curves; lots of knitting! and math! check it out. I can't get a direct link, so I'm quoting here (check out the original post, on June 26, for the justification):
And so I present my method for knitting a circle that lies relatively flat, or at least as relatively flat as something knit entirely in stockinette can be:
CO some stitches on dpns. Join for working in the round.
Rnd 1: k, inc 4 sts relatively evenly spaced
Rnds 2 - 4: repeat rnd 1
Rnd 5: k, inc 5 sts relatively evenly spaced
Repeat rnds 1-5 until circle is desired size, switching to a circular needle as desired.
Perfectionists may choose to inc 4 instead of inc 5 in rnds whose number is divisible by 100.
The reason that the increases are linear (i.e. inc 4.19 sts every rnd) is that the number of sts is a linear function of the circumference, which is a linear function of diameter, which is a linear function of the number of rnds. As a knit stitch has height:width as 2:3, the number of sts to increase each rnd is 2&pi(2/3). For some other stitch, multiply 2&pi by its height:width ratio to determine how many sts to increase each rnd in order to knit a circle.
And for the order-of-magnitude back of the envelope scientists, myself included, increasing 4 sts each row works just fine. It's just a cat bed!