I love knitting math. I realize that's geeky, but I really get a buzz off trying to figure out how many stitches, rows, increases or decreases I need to make to get the result I want. I think it's good mental exercise, and it's very satisfying.
Only problem is, math doesn't love me so much. I make a lot of mistakes! Fortunately I'm not so miserable about the frogging, otherwise I'd be sad. In my case I think "measure 85 times, then ask someone else to check your measurements, then cut, then redo it because even after all that you messed up" should replace "measure twice, cut once."
Here's some of my notebook for Madeleine, the little matinee coat I'm making for a certain baby about to be born in Cornwall. You can see the original design sketch (I'm no artist, sorry!) at the center bottom, and lots of figuring on the other sheets. With lots and lots and lots of erasures where I had to re-figure. And some cross-outs.
Even after redoing my math a few times, I found a number of things went wrong when I tried to make the sleeve:
1) I simply screwed up, and used the desired # of rows for the wrist-to-armpit length as the desired rows to the shoulder. Whoops.
2) I forgot to account for the fact that the paired increases I use tend to shorten the fabric in that location (underarm, in this case).
3) It turned out that, knitting in the round, my stitch count per inch was only a teensy bit smaller than when knitting flat — but my row count was way different.
4) Also, I may have accidentally used the measurement of the hypotenuse of a triangle for the measurement of the opposite side.
So this was my first sleeve. Whoops. A fine short sleeve (and yay, I did a pretty darn good job shaping the sleeve cap) but.. not really the long sleeve I was after. Tee hee.
I knit a couple alternate sleeves to the armpit, one (the upper) in the same US #4s/3.75mm I'm using for the (flat-knit) body and one (the lower) in US #5s/4.0mm. The gauge difference is subtle, but present. And I like the fabric on the #5s better, so I'm sticking with that for the arms. (Also, these ones are the right length.) Just have to knit a sleeve cap and redo the other arm now...