03-16-2007, 07:48 PM #1 Lighting57 Working the Gusset     Join Date: Sep 2006 Location: South Eastern, USA Posts: 1,007 Thanks: 437 Thanked 163 Times in 121 Posts PI Theory Can anyone give me the formula for PI? I'd like to try my hand at designing one of these shawls, but I haven't been able to find a source that explains the mathimatics of figuring PI.

 03-16-2007, 10:43 PM #2 five_six Turning the Heel     Join Date: Dec 2006 Location: Brissy - Australia Posts: 702 Thanks: 10 Thanked 17 Times in 14 Posts well i thought PI was a mathematical constant, and that it is still trying to be figured to it's correct decimal value, but now instead of mathematicians and philosophers doing it, we have computers (it's gone from having 35 decimal places to over 100,000,000). It is the expressed ratio between the circumference of a circle and it's diameter, from what I remember from maths... and you would simply just use PI (as we currently know it 3.1416). So technically, i guess i'm trying to say, you can't figure PI, or if you do, you'll be spending an awful long time on it (someone spent their whole lives!), but you can use PI to figure things. I probably haven't helped you out much at all! EDIT: to be clearer for you. PI will always be the same no matter what size circle you are using... you divide the circumference of a circle by it's diameter, and you will get PI, but as this is always the same, this is why i said to use 3.1416 - here are some more complex formulas for pi: Vieta's Formula 2/PI = 2/2 * ( 2 + 2 )/2 * (2 + ( ( 2 + 2) ) )/2 * ...c Leibnitz's Formula PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ... Wallis Product PI/2 = 2/1 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * ... 2/PI = (1 - 1/22)(1 - 1/42)(1 - 1/62)... Lord Brouncker's Formula 4/PI = 1 + 1 ---------------- 2 + 32 ------------ 2 + 52 --------- 2 + 72 ... (PI2)/8 = 1/12 + 1/32 + 1/52 + ... (PI2)/24 = 1/22 + 1/42 + 1/62 + ... Euler's Formula (PI2)/6 = (n = 1..) 1/n2 = 1/12 + 1/22 + 1/32 + ... (or more generally...) (n = 1..) 1/n(2k) = (-1)(k-1) PI(2k) 2(2k) B(2k) / ( 2(2k)!) B(k) = the k th Bernoulli number. eg. B0=1 B1=-1/2 B2=1/6 B4=-1/30 B6=1/42 B8=-1/30 B10=5/66. Further Bernoulli numbers are defined as (n 0)B0 + (n 1)B1 + (n 2)B2 + ... + (n (n-1))B(N-1) = 0 assuming all odd Bernoulli #'s > 1 are = 0. (n k) = binomial coefficient = n!/(k!(n-k)!) I think this may be a little too detailed for you tho You may have to actually get an EZ book for her PI calculations, I couldn't find much online about using her technique (prolly cause the content is copyrighted) __________________ Dee If a little dreaming is dangerous, then the cure is not to dream less, but to dream more... to dream all the time! - Proust currently recruiting for the war i am waging on time, there will be many casualties, but we will be victorious
 03-16-2007, 11:45 PM #3 of troy Turning the Heel   Join Date: Dec 2006 Location: queens Posts: 715 Thanks: 4 Thanked 287 Times in 215 Posts Pi shawl are a form of binar math. this is totally 'standard math' --but not usually applied (or workable to create circles!)in standard math. but you have to remember that knitting has a 2:1 ratio (garter) and 3:4 ratio (stocking knit) and yet another ratio for the *K1, YO rows! and most formulas for creating a circle (on a cartesian plane) do not have these pecuilar ratios (but rather have a 1:1 ratio. so things work out differently in knitting than they would on standard graph paper-(which is why knitters use knitters graph paper, with its rectangles, not squares!) a basic Pi shawl "formula" every time the number of rows doubles, double the number of stitches. (start with 4 (you can start with other number, and a similar pattern appears, it is most evident with 4 (or 8) cast on 4 row 1 4stitches row 2 (you've double the number of rows, now double the number of stitches-8 stitches. row 3 -8 stitches row 4 (double again, so double again--16 stitches) row 5, 6, 7, --16 stitches row 8 --double stitches (32 stitches)row 16-- 64 stitches but if you just increase 8 stitches everyother round, you get to the same numbers (of stitches) at the same rows. row1-- 4 row 2-- 8stitches row 3-- 8 row 4-- 16stitches row 5-- 16 row 6-- 24 stitches row7-- 24 row 8-- 32 stitches row 9-- 32 row 10-- 40 stitches row 11-- 40 row 12-- 48 stitches row 13-- 48 row 14-- 56 stitches row 15-- 56 row 16-- 64 stitches it is binaray/hexidecimal math at its most basic! You don't even have to know or understand binary or hexidecimal --just look at row 8 or row 16 in each "pattern" in both cases, you end up with the same number of stitches. both of these patterns work, because, in the end, the increases are the same! NOTE: both patterns require YO's for the increase, not another type of increase. many, many circular shawls work with 8 increase every other round.. and Pi (the knitting pi shawl) is a that ratio simplified. (i am an amuteur math geek when i am not knitting) __________________ my blog I'm Oftroy on Ravelry
 03-17-2007, 09:43 AM #4 Yarnlady Turning the Heel     Join Date: Jun 2006 Location: Knitting at my computer Posts: 909 Thanks: 26 Thanked 125 Times in 106 Posts Gee, aren't you glad you asked? __________________ LizzieK8 (Ravelry Handle) http://lizzysends.blogspot.com/
 03-17-2007, 02:24 PM #5 Lighting57 Working the Gusset     Join Date: Sep 2006 Location: South Eastern, USA Posts: 1,007 Thanks: 437 Thanked 163 Times in 121 Posts Thanks all. That helps a lot, more so than any of the sites I searched. Those that did give some form of explanation seemed to be talking out of both side of their mouth. It'd be great if there were a site that had downloadable patterns (that used Pi). Then the mork would be done for me.
 03-18-2007, 12:50 PM #6 KnitClickChick Turning the Heel     Join Date: Dec 2006 Location: In my own little world Posts: 606 Thanks: 146 Thanked 140 Times in 103 Posts I got a book from the library a few weeks ago, and there was a PI shawl from Elizabeth Zimmermann. Math is not my thing at all, but this I could understand. Her explanation: It is just the circumference of a circle doubling itself as the radius doubles. For example: cast on 9 stitches and knit one round. Then, increase stitches to 18 and knit two rounds. Next, increase stitches to 36 and knit 4 rounds. (The number of stitches was increased by k1, yo) I really didn't feel like making an entire shawl, only to have something go wrong, so I just practiced by making a doily. Pretty neat technique. __________________ I knit, therefore, I smile Wish List Clapotis Another felted bag Mrs. Beetons Wristwarmers On The Needles: Silver's Palindrome Scarf - in Patons SWS Natural Pink Feather and Fan Shawl - in Estelle Cadenza

 Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts vB code is On Smilies are On [IMG] code is On HTML code is Off
 Forum Jump User Settings Private Messages Subscriptions Who's Online Search Forums Forums Home KnittingHelp.com     General Knitting     How-to Questions     Pattern Central     What'cha Knittin'?     Knit-Alongs     Charity Knitting     Creating Yarn: Spinning, Dyeing, etc.     Crochet!     Blog Threads     Knitters Knear You     Buy/Sell/Swap     The Lounge