1/28/2003

Ginn asked where one goes to learn knitting math, and the answer, for today at least, is right here! This lesson is not really lesson 1 -- but it's the one I just did, so here it is:

Knitting and the Pythagorean Theorem

This is the Pythagorean Theorem. You learned it in high school geometry. My teacher was Mr. Marcy. He loved Albert Einstein and Willie Nelson. We had in-class birthday parties for each. I liked Geometry much more than Algebra or Calculus.

This is your sweater on the Pythagorean Theorem. Any questions?

Here's the big question: How do I make the decreases on the body and the sleeves so that the raglans match up?

First the bits we do know: I know about how wide the sleeve opening needs to be. I'll call this number "A" and say that it needs to be about 5 inches for a baby sweater*. I know how wide to make the bottom of the sweater and the neck opening. Let's say d = 11 and e = 7 (e = 7 because this is a modified boat neck).
Now how to use this information for truth, light and righteousness?

Sharpen your pencils and get out your calculators because it's math time! Let's solve for B and C so we know where we stand.
d - e = 2B. So, 11 - 7 = 2B and B = 2.
To find C, we use the Pythagorean Theorem: The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse... or something like that.
A ² +B² = C²
(5 x 5) + (2 x 2) = C²
25 +4 =29 = C²
So, C = 5.4 (more or less)

Sometimes you can just do the decreases the same on the sleeves and the body, but that wouldn't work in this case because I need to get rid of more stitches on the sleeves than I do on the body. How do I know this?

There is a second right triangle on the sleeve.
If the decreases are the same on the body and the sleeve, then B is the same on the body and the sleeve and therefore B is the width of my sleeve.
BUT B is only 2 inches! There's an extra inch at the cap of the sleeve and we add that in, but that still only gives us a sleeve that measures 5 inches all the way around (2B + 1 = 5) That is not wide enough for the sleeve. What to do?

We know that C must be the same on both the sleeve and the body since we want them to match up when we sew them together. C = 5.4. 2B + 1 is the total width of the sleeve and we want that to equal 10, so B = 4.5. Now once again, we turn to Pythagoras.
A² + B² = C².
A² + (4.5 x 4.5) = (5.4 x 5.4)
A² + 20.25 = 29
29 - 20.25 = 8.75
A = 3 (more or less)

So, now we know all the measurements for the sleeves and the body. Next time, the rubber meets the road: How to turn these numbers into a knitting pattern.

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