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Saturday, 28 November 2015

Triangle Shawls and fun with algebra

by madorville


While knitting a triangular shawl where one starts with 7 stitches (ignore the set-up rows which use a trivial amount of yarn in the grand scheme of things) and increases four stitches every right side row, if N is the number of rows that have been knit then the total number of stitches done is N² + 5N. (now that I think about it, I am guessing one could derive this from a simple area of triangle formula.)

How does one use this delightfully compact formula? Well, I have knit 10 pattern repeats so far. With 26 rows to prepare for the main pattern, 10 rows per repeat, I have knit 126 rows. Therefore I have knit 126*126 + 5*126 = 16,506 stitches in total.

My scale says this weighs 55 grams, or about 300 stitches per gram.

Looks like plenty of yarn for another pattern repeat or two. Keeping in mind that the finishing will require 12 rows, how much yarn can I expect to use if I knit a few more repeats?

11 repeats: N = 126 (rows so far) + 10 (11th repeat) + 12 (border/finishing) = 148

148² + 5*148 is 22,644 stitches. At 300 stitches per gram, this will use 76 grams of yarn.

12 repeats: N = 158 Total Stitches = 25,754 or 86 grams

13 repeats: N = 168 Total Stitches = 29,064 or 97 grams of yarn.

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