I want to knit a flat circle (about 10" across) and not use short rows. I've looked at a couple of dishcloth and doily patterns and am trying to figure out the math used to get it flat.
All the ones I've seen have you start in the middle with a few stitches on DPN. I'd rather start on the outside using a circular and then graduate to DPNs as you get closer to the center. (I know, I just HAVE to be difficult!) I just think it would be easier.
I know you must decrease with each round, but by how much? If I start with, say 100 sts on a circular, is there a formula I should use to know when to decrease - Knit 2 together every X stitches?
On Thu, 10 Mar 2005 13:25:51 -0500, Gallagher babbled something about:
I just *know* that either Sonya or Wooly are going to beat me to the answer while I do the math.... but if they don't... I'll get back to ya, Abi! (Personally, *I'd* start in the middle....)
Working from the outside in you should treat it like the crown of a tam, which, IIRC, uses double decreases (s2kw, k1, p2sso) every other round at 8 points.
Its easier to work from the inside to the outer edge, imo.
On Thu, 10 Mar 2005 13:25:51 -0500, "Gallagher" spewed forth :
I knitted a square from the inside out, for one of the 6x6 exhanges. It became a star, and no matter how hard I tried doing it from the inside out, still the four edges would bow in to the center. I then took the pattern and started at the outside on indeed double pointed needles, I used 5 I think. The square became nice and flat with straight edges. I could see right away if it was going to lay flat or not, and added or decreased the stitches on the four corners. Maybe it would work for a circle as well. Sample and see if it works. I got my pattern from the Readers Digest complete guide to needlework
Abi i feel with you that starting on the outside is better for ME , Try and find a pattern that works regulary from the middle outwards and do it the other way ,, strat by the maximum end number of stiches ...You might need 2 circulars ,,,i will think about this and see waht i can work out . mirjam
I was hoping to start from the outside of my disc and work in because my arthritis somes makes starting a small circumference on DPN difficult. I have used the two circular method, and may try that, then graduate to DPN after a few rows, then to circulars as the circle expands.
What I want to avoid is doing a large octagon. I'd like this circle to be, well, a circle - no points. If I ever master the "perfect circle" I'll post my findings.
The Prophet Gallagher known to the wise as snipped-for-privacy@stargate.net, opened the Book of Words, and read unto the people:
I'm coming to this from the point of view of crochet rather than knit, but the same assumptions should carry over fine. Working from the outside in and working from the inside out should (in theory) be fairly symmetric, since a K2tog working inwards is morally equivalent to an increase working outwards.
No valeu of X in your above suggested method, however, will work, since you'll be putting in more decreases in the outer rounds than the inner rounds. To figure out the right approach, we basically need to consider what happens as we reduce (or increase) the diameter.
Suppose a stitch has height h and width w, and the work at the moment has radius r. The circumference of a circle of radius r is 2*pi*r, so since you want all the stitches in a round to have total length of the circumference of the round, we need n*w = 2*pi*r (n being the number of stitches), so n = 2*pi*r/w. Then, on the next round, the radius will be r+h (if increasing) or r-h (if decreasing), since we've added some width to the work and changed the radius of the round we're working on. So this round needs to have 2*pi*(r+h)/w or 2*pi*(r-h)/w stitches; that is, the number of stitches on this round is more or less than the previous round by 2*pi*h/w, so that's the number of increases/decreases you're going to want.
Some notes on this: first, it doesn't depend on r, so you're going to want the same number of increases/decreases on each round. Also, it doesn't actually depend on h or w, but rather on the ratio between the two, so you don't have to laboriously measure a single stitch, but can instead make a gauge swatch (say, 10 stitches, 10 rows) and measure the ratio of the height and width of that.
As an example, if your gauge swatch is perfectly square, or slightly wider than it is tall, then h/w must be 1 or slightly less than 1, so
2*pi*h/w is approximately 6 and you'd want about 6 increases or decreases per round.
As a final note, the relation C=2*pi*r describes the fact that ordinary space has zero curvature. Spaces in which C2*pi*r then the space has _negative_ curvature_ and cannot be faithfully embedded in ordinary 3D space but we try to do so anyways (this corresponds in crochet and knit to overincreasing, which can cause the edge of the work to be oddly scalloped or ruffled). The control crochet and knit provide in adjusting local curvature have been exploited for mathematical demonstrations, and have been written up on at least two occasions:
David Henderson and Daina Taimina, "Crocheting the Hyperbolic Plane", Math. Intelligencer, v. 23 (2001), n. 2, 17--28; and
Hinke Osinga and Bernd Krauskopf, "Crocheting the Lorenz Manifold", Math. Intelligencer, v. 26 (2004), n. 4, 25--37.
Well, I am humbled! More info than my little brain can process.
At knittersreview.com, I found a bit of more simplified information - "To knit a circle---any circle for any reason--- all you have to do is have 8 increases/decreases every other row. You can space them anyway you wish as long as they average 4 per row. For example, 8 every other row, 16 every fourth row, etc. "
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