Wednesday, 5 January 2011

True Pi Shawl

I'm using the Elizabeth Zimmerman method to make my Pi Shawl (cast on 9, work 1 row, k1 yo for a row, work 3 rows, k1 yo for a row, work 6 rows,  k1 yo for a row, work 12 rows etc).

The issue I have with this is (as the fair-isle version highlighted) as the number of rows between increases grows, the amount that the stitches are stretched width-wise increases. This is because the relationship between the circumference (stitch count) and radius (row count) is linear. Stitch count = 2 * Pi * Row count.
By not increasing every row... we are short stitches until we do an enormous catch up at the next increase.

Boring proof below:

Row 1: Stitch count should be 2 * Pi * 1 = 6 (actual = 9)
increase row =
Row 2: Stitch count should be 2 * Pi * 2 = 12 (actual = 18)
Row 3: Stitch count should be 2 * Pi * 3 = 18 (actual = 18)
next increase row =
Row 6: Stitch count should be 2 * Pi * 6 = 36 (actual = 36)
Next increase row =
Row 13:Stitch count should be 2 * Pi * 13 = 78 (actual = 72)
then we knit 12 rounds. on the last of these
Row 25: Stitch count should be 2 * Pi * 25 = 150 (actual = 72) 

At row 25 we have less than half the stitches we should have  - no wonder the stitches are stretched so much.

I'm going to experiment with the following formula for the second shawl
Cast on 6 stitches
knit one row 
increase in every stitch (12 stitches total)
Increase in every other stitch (18 stitches total)
increase in every 3rd stitch (24 stitches total)
increase in every 4th stitch (30 stitches total)

and after a while it can just be increase 6 stitches randomly every round.

No more stretched stitches, no more bands of increases. Just how to place the increases so they don't 
1) line up turning it into a hexagon
2) end up looking like semi-random moth holes!


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