Humiliating knitting geometry question

[neadods]

How sad is it that I can't work out the number of stitches along the diagonal of a square when I know the number of the stitches along the two sides? (ETA: 40 stitches per side. In theory. It can be argued that maybe the reality is 40 stitches on a and 39 for b, depending on how you count...)

I understand that what I'm looking for is the hypotenuse of a right triangle. I understand that a2 + b2 = c2, which reduces to a + b = c. I understand that as I work on the problem from the other angle (casting on in the corner and adding a stitch every row) the preliminary numbers of stitches along side (a and b) vs. number of stitches on needles (c) is exactly a + b = c.

I also understand that when I worked a mitered version of the same square, I cast on a + b and then reduced 2 stitches every other row, so that by the time I was knitting along c, it was well under the sum of a and b.

And that's when the cognitive dissonance hits.

I would like to be able to provisionally cast on along the diagonal, reduce every row to one corner, pick up the live stitches, and reduce every row to the other corner. It would be easier, and thus more zen to do. I'm not doing too well at picking up the "knit in the bar" increase, although that's the only one that gives me the look I want (I've tried the classic knit-front-back and I don't like the look for what I'm doing).

However, I cannot cast along the diagonal until I know what the diagonal properly is...

Comments

[doyle_sb4.livejournal.com]

Actually, I don't think you need to work out the hyptonenuse at all. Say your square is 10 by 10 - you're just dropping one stitch each time. Representing this with *s:

**********
*********
********
*******
******
*****
****
***
**
*

a = 10
b = 10
c = 10