Lost Arts studio

A lot of the fiber arts I enjoy are things like tatting, netmaking, chair caning, and even weaving, where people will come up to me when I demonstrate and solemnly tell me, "That's a lost art."

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Location: SW Outer Nowhere, Michigan, United States

On the Internet, nobody knows you're a chicken. (With apologies to Peter Steiner.)

18 February 2008

Sock It To Me, Baby (Yarn)

I had a confusing day today, like a second Sunday.

My husband, who works for the National Guard, had "Presidents' Day" (otherwise known around here as "yet another fake government-employee holiday") off. Coincidentally, so did our son.

So today was a day with homemade waffles for breakfast, no mail, and my two guys home all day. Must be Sunday, right?

I've knitted socks with both worsted-weight and baby-yarn acrylic, so I'm not worried about how they'll fit. Over the last couple of years, I've worked out how to knit a short-row heel that fits my foot nicely. The hard part is explaining it!

If you cut up a commercial sock with a short-row heel, this is what you get:

Other names for the short-row heel are "hourglass heel" and "wedge heel", emphasized in red on the right. I've cut the heel apart to show the shape that needs to be knitted.

Here is a blown-up view of the wedge that fits me. The 2" wide by 2-1/2" long rectangle in the center is the strip that goes underneath my foot, from the instep to the back of the heel.

It's 2" wide because that is the width of my heel, right at the back where the bottom of this rectangle falls when I wear it.

It's 2-1/2" long because my foot is 9-1/2" long, and I stop knitting a plain tube when it is 7" long, the length of my foot from the toe to where my instep turns into my ankle, taken on the top of the foot.

But where does the 2-1/8" to either side of the top of the rectangle come from?

This one I figured using trigonometry -- look, Mom, all that math I took and I'm actually using some of it!

The length of the diagonal of the triangle in my diagram is 3.28". I measured my foot from the back of the heel to the "waggly spot" of my ankle bone: this measurement is about 3-1/4". So I actually figured the 2-1/8" in reverse, using the Pythagorean theorem (x2 + y2 = r2).

I had r = 3-1/4", the measurement of the diagonal. I had y = 2-1/2", the measurement of the height of the triangle. So that gave me x2 + 6.25 = 10.5625.

First I solved for x2: x2 = 10.5625 - 6.25 = 4.3125. (Did they teach you to show your intermediate steps? Okay, subtract 6.25 from both sides: x2 + 6.25 - 6.25 = 10.5625 - 6.25) This gave me x2 = 4.3125. My handy pocket calculator says the square root of 4.3125 is about 2.08". Since it's usually tough to tell when I have 8 hundredths of a knitted stitch, and since my 12-1/8" heel is lot bigger than my 9-3/4" foot, I bumped it up to 2-1/8".

And the proof of the math is in the knitting:
The pink-and-purple sock was knitted in the spring of 2006, so this sock heel has had two years of wear.

I knitted the blue-and-purple (and pink & green) socks last summer, so the sock toe is around six months old.



Blogger Knitting Linguist said...

OK, I am now officially worried about all that time you're spending under cloud cover up there. ;) I'm so impressed that you're figuring out in a rational way what I figure out by knitting, swearing, ripping, and repeating as necessary. I'm off to show this to my husband to prove that knitting would indeed be interesting to his mathematical mind.

6:16 PM  
Blogger Bells said...

can we have more pictures of snow? I understand those. :-)

4:07 AM  
Blogger Kathleen C. said...

Thanks for the short row heel maths... I like the look of those (especially with those handpainted, self striping yarns), but I've never liked the way they fit my foot. I'll have to see if using your formulas can get me a better fitting sock.

And thanks for the Cornell bird link. It's filled with info! Maybe now I'll be able to name all those LBBs (little brown birds) in our yard.

1:37 PM  
Blogger Knit - R - Done said...

I'm more of a knit-the-sock-then-find-a-recipient kind of girl. Kudos to you!

4:58 PM  
Blogger Sharon said...

I think I might take another look at this post when my brain isn't so tired. Maybe then I'll understand it ;)

I'm guessing that you like to listen to that one podcast that I came across once... http://math4knitters.blogspot.com/

I've only listened to a few episodes myself, but definitely found them very helpful!

3:08 PM  

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