Extrapolating a hat to different sizes

In writing up the pattern for the Cozy Cabled Hat, one of the things I got the biggest kick out of was figuring out how to fit different sizes. Finally, something fun to do with math! I'm actually exaggerating, I'm one of those freaks who likes to do math (please don't throw your rotten fruit at me--I'll help you balance your checkbook if you'll put down that torch). For hats, it's relatively straightforward: if your gauge is X in units of stitches/inch and your head circumference is Y in inches, multiply X times Y and you know how many stitches you need to make it around your noggin. In formula form:


Full disclosure: I made the formula picture in Gimp, thinking it would be a great time to work on my graphic design skillz. I thought maybe I could make it pretty and colorful and loveable, and after working on it for 30 min this was as far as I'd gotten. Graphic designers, I bow to you. To atone for this crappy, boring picture, here are some puppies!

Aww.

Aww!

AWW!

There, now don't we all feel better? The same principle of the formula also applies to rows. It was easy-peasy on the Cozy Cabled Hat; the extra stitches I added for the larger sizes meant extra rows when it came to decreasing at the top. I also designed it with a fold-up brim--which added a LOT of leeway--so I didn't worry about length too much (i.e. at all). On the Infinite Cabled Hat, I used a specific decreasing scheme to get the cables to appear to continue, even though half of them were gone. I needed to make sure that it would translate to the larger sizes.

But first, how many inches of length does one need in relation to the circumference of their head? Assumption #1: The human head is a sphere (a ball, basically). Assumption #2: A hat should cover approximately half of the sphere. This leads to the conclusion that length from the top to bottom of the hat should be approximately half that of the circumference of the hat. I was hoping that I could get pi involved (mmm pi) but it wasn't even that complex.

Now, for the task at hand: for every one inch increase in circumference, a 1/2 inch increase in length was required. The problem: my row gauge was 8 stitches/inch, and the pattern repeats every 8 rows. See what I'm driving at here? The small and large sizes work out perfectly, but the medium size ends up cabling smack in the middle of the decreasing, which we just couldn't have. I pondered and pondered. I started to think of it as AC and the Angry Half-Inch. And then it came to me, as almost all of my knitting solutions do, right before I was about to fall asleep (seriously!)--stick that extra junk on the bottom half of the sucker instead of the top. And they say today's youth don't have any critical thinking skills.

I'm going to try to get the various sizes tested through a Ravelry group of free pattern testers. I've tried to be a tester for others a couple of times, but nothing has gone all the way to fruition. It seems like a neat system though. I feel a bit silly asking for people to try out my little endeavor, but nothing ventured, nothing gained (it also doesn't hurt that internet tends to be anonymous, so no one can laugh directly at my shame).