Back in June I finished a cool pair of socks using the number Pi as a means to devellop an interesting stripe sequence. I realize that the explanation on what I did and how Pi is involved might have been a bit cryptic. A couple of people have asked questions about it over time so this entry is supposed to clear up some questions and make up something that at least loosely resembles a pattern. That way I can even put it up on Ravelry as a pattern ;o)
Use any fingering weight sock yarn of your liking. It can even be a heavier 6-ply sock yarn if you want something that knits up faster. Gauge doesn't really matter here as long as you know how to re-calculate things to get a sock that actually fits.
I chose good old Schachenmayr nomotta Regia Uni/Solid 4-ply/4-fädig in chocolate brown and green. One 50 grams skein of each should do. For the stripes to really pop you'll probably want to choose two colors that have a high contrast. How about brown/yellow, black/white, turquoise/magenta or dark red/pink?
I like to knit Regia 4-ply on 2.5 mm needles but I am told there are all kinds of knitters out there. You might be a loose knitter and 2.25 mm needles give you better results for your socks. Or ask my sis. She knits really tight so 2.75 mm DPNs are usually the tool of her choice.
We start out with Pi’s numerical value truncated to 50 decimal places: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510. Pretty cool number, eh?! You could start out knitting as the digits appear above: 3 rounds color A, 1 round color B, 4 rounds color A, 1 round color B and so on. Alas, we would run into a problem as soon as we hit the first zero, wouldn't we? "Zero rounds of color A/B"?! You'd get one wide stripe and couldn't decode it back into the two digits it was composed of.
To compensate for that problem we go with a simple rule: Add 1 to each of Pi's digits so that even 0 ist represented accordingly.
Color A: 4 rounds
Color B: 2 rounds
Color A: 5 rounds
Color B: 2 rounds
Color A: 6 rounds
and so on
While working your stripes knit your socks in your favored basic sock pattern. You can either do them toe-up or cuff-down or whichever way suits you. I usually work mine top-down with a cuff in 1x1-ribbing for 15 to 20 rounds, switch to plain stockinette stitch until the sock measures about 15 to 20 cm (6 to 8'') and work a flap-heel. For the heel I stopped working stripes but chose to knit it in the brown yarn instead. As soon as the heel was turned and stitches for the instep were picked up I started working the stripes again. The toes I also did in plain brown and closed them using kitchener stitch.
My second sock continues where the first one left off. This way my socks represent Pi as 3.14159 26535 89793 23846 26433 83 (1st sock) 279 50288 41971 69399 37510 582 (2nd sock). Of course the stripes will not necessarily work out evenly so should you decide to follow my example you might have to live with socks where one leg is a couple of rows longer or shorter than the other. Same goes for the foot. I don't mind but if you're a stickler for such things you might want to just work two socks with the same stripe sequence. Or you could probably do some counting in advance to figure out which sequences of digits give you the same checksum.
While working the stripes I didn't cut the yarn not in use but carried it up on the inside making sure it didn't pull too tight or wasn't hanging too loosely. That way you can spare yourself a hell of a lot of sewing in ends later. Where the colors change a little jog appears that seems to drive some people nuts. Again, I don't mind. I did nothing to avoid it. There are all kinds of tips out there on how to minimize "The Jog" if you actually care about it.
I'm finishing up a Pi hat as my son's Christmas gift! The colors (seven of them) match the scarf I made last year. I stopped at 3.14159, though, so that the stripe sequence could repeat. Thanks for the chart (and the next four digits). Pi socks for Christmas 2009?