Saturday, April 28

Trapezoid Shawl Formula!

An update on the shawl calculations. We aren't knitting triangles, we are knitting trapezoids! That explains the formula Susan and I each derived.

Recall from Algebra I: Area of trapezoid is 1/2(Base1 + Base2)*Height

In our cases, remember N = number of rows
Base1 = 7 stitches
Base2 = 2N+3 stitches
Height = N

voila! Number of Stitches = N² + 5N

Oh, why didn't I do this immediately instead of working out the sum from i = 0 to N of (7 + 2i)? Just goes to show that too much mathematics is a dangerous thing.

Kmkat, the Gaussian addition thing is from a (probably apocryphal) story of little smart ass future famous mathematician Gauss as a child and a teacher who was fed up and wanted some peace and quiet. She asked the class to sit quietly and add all the integers from 1 to 100. Gauss figured out almost immediately that the answer was 5,050. So much for the teacher's quiet afternoon.

As for me and my shawl last night I completed pattern repeat number 11. According to my calculations, I have knit 74.4% of the shawl and according to my scale I have used 73.8% of the yarn! It will be close. That's using the 12 repeats/88 grams. Have to admit I am tempted to work some more on untangling the 12 grams and adding an extra repeat. If all goes well, if I can manage to untangle the whole thing, I can complete 13 pattern repeats and end up with about 2 or 3 grams left over.

3 comments:

kmkat said...

Thanks for the Gaussian explanatin. The shawl is lookin' good!

Dorothy said...

Your shawl is looking beautiful. Is that netting around your yarn cake?

Dorothy said...

Yes, that it netting around the yarn. A homemade yarn bra. I usually use knee high panty-hose, but this is just the net tube that some vegetables come in, onions and the like. In the case of the Sea Silk, having some sort of yarn bra is Very Important. It is slippery stuff.