Saturday, October 22, 2011

Quick Post with Math Saturday, October 22, 2011

I saw this cool book, The Sock Knitter's Workshop , so of course had to buy it.  It has many things that are new to me, like different shaped toes and heels, picot cuffs, etc, that you can mix and match into your sock designs.  

I have one complaint about it, though.  Everything is given in numbers instead of equations.  For instance, at the back of the book are some charts for heels and toes using different yarns such as  "Heel Sizes with Fingering-Weight or 4 Ply Sock Yarn."  They then give the number of stitches for every size from children's size 5 to women's size 15.  Wouldn't it be easier to give measurements for those sizes, then designers/knitters can figure out how many stitches to cast on with a simple equation?

number of stitches to cast on = width in inches X gauge in stitches/in

The number of stitches varies with your gauge AND the size of the sock you are knitting.  If you can't get your gauge exact, the sock will not fit.  Let's say you are off by 1/2 stitch.  You are knitting 7.5 stitches/in instead of 8 st/in.

Reversing my little equation I gave above:  Number of stitches cast on / gauge per inch = Width in inches

with a gauge of 7.5 st/in and 64 stitches in the pattern:
64 / 7.5 = 8.53 inches width

with a gauge of 8 st/in and 64 st in the pattern:
64/8 = 8 inches width

this is .5 or 1/2 in difference in the width of the sock with just a 1/2 or .5 difference in stitch gauge.  If the gauge is off by 3/4 of a stitch, the difference is greater:

 64/7.25 = 8.82758  which is more than 3/4 of an inch difference. 

Below that line, there is a line that says how many stitches should be on each needle. For instance, if you have cast on 64 stitches, then using 4 needles:  16 stitches/needle.   Really?  Knitters can't divide the total stitches by the number of needles?

Anyway, here is some of the math for the foot part of Hannah's Hermione socks:

(sorry that I switch back and forth between fractions and decimals)
Foot length: 9.5 in
heel & gusset 3 5/8 in
Toe 19 rows (from pattern)

foot length - heal & gusset length :  9 4/8 - 3 5/8 = 5 7/8in
5 7/8 in x 12 rows/in = 70.5 rows
70.5 - 19 = 51.5 rows of foot pattern (rounding down to 51)
the pattern is 4 rows, so 51/4 = 12 3/4 iterations before beginning the toe decreases.

This math is not hard.  I think I will look at the stitch charts and try to make more equations for myself.  These can be used in EVERY occasion, truly tailoring each sock, needle, yarn combination to fit the particular foot.  The only problem comes with pattern.  If you cannot get the the gauge (I never seem to be able to do this), you will have to add or subtract from a pattern, changing the look a bit.

C. A. Losi (former Math teacher)

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