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.