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21 May 2008 @ 08:14 am
Sometimes I really over complicate things  
For example, I was trying to figure out some math for shawls. I got all caught up in trying to make sense of Pythagorean formulas for right angle triangles, and lost sight of a simple fact that really simplified the math. Worse? I KNEW it. It's a mathy thing I had figured out a while back, but for some reason, didn't remember and it took a certified math genius to point out the silliness.

So.. I was trying to work out the length of a shawl from the hypotenuse.
and somehow completely forgot to factor in the fact that the triangle is really half a square, so the length is the hypotenuse/2.

You can figure out the diagonal of a square by multiplying one side by 1.4142. Which is really probably more decimal points then you need for crocheting, but I did check this, a square that's 3.5 inches across is just under 5 inches on the diagonal. So with that square, if I want a shawl that's 3 feet long and 6 feet across the hypotenuse (a nice size I think).. 36/4.9= 7.3469 (still more places then you need, this is a shawl, not rocket science or architecture) OR 7 squares on the diagonal long, and 14 half squares (triangles) across, which winds up being a little shy of 6x3, but that's okay. A couple rounds of single crochet will fix that.
So then creating the graph. The total shawl, working with half squares and squares that size is 91 full squares and 14 half squares. Click on graph for large graph.

So for that shawl, describing the squares from the inside out..
Half squares-
4 purple-orange-red
2 red-yellow-orange
2 orange-green-yellow
2 yellow-blue-green
2 green-purple-blue
2 blue-red-purple

Squares-
26 purple-orange-red
5 red-yellow-orange
9 orange-green-yellow
13 yellow-blue-green
17 green-purple-blue
21 blue-red-purple
All the squares bordered with black yarn, 4 rounds, 3 rounds of the granny square, plus a border.

This is the pattern for the square I measured. If you are doing it in multiple colors, break off at the end of each round, and join new color in at the ch 2 corner to work the next round.
Simple Granny Square- 3 rounds with a border

With a size G hook and worsted weight yarn.

Chain 6, sl st to join
Rnd 1- ch 3 (counts as first dc) 2 dc in ring, ch 2, 3 dc in ring, ch 2, 3 dc in ring, ch 2, 3 dc in ring, ch 2, sl st to 3rd chain of beginning ch 3.
Rnd 2- sl st to ch 2 space, ch 3, 2 dc, ch 2, 3 dc in same space, skip 3 sts, 3 dc, ch 2, 3 dc in next space,skip 3 sts, 3 dc, ch 2, 3 dc in next space,skip 3 sts, 3 dc, ch 2, 3 dc in next space, sl st to join to 3rd ch of beginning ch 3.
Rnd 3- sl st to ch 2 space, ch 3, 2 dc, ch 2, 3 dc in same space, skip 3 sts,3 dc in next sp, skip 3 sts,3 dc, ch 2, 3 dc in next ch 2 space, skip 3 sts,3 dc in next sp, skip 3 sts,3 dc, ch 2, 3 dc in next ch 2 space, skip 3 sts,3 dc in next sp, skip 3 sts,3 dc, ch 2, 3 dc in next ch 2 space, skip 3 sts,3 dc in next sp, sl st to 3rd ch in beginning ch 3
Rnd 4- ch 1 (doesn't count as first stitch) sc in each st, 4 sc in ch 2 corners. sl st to join.

Half square-
Ch 6, sl st to join
Rnd 1- ch 3 (counts as first dc) 3 dc in ring, ch 2, 4 dc in ring
Rnd 2- ch 3, 3 dc in same stitch, skip 3 sts, 3 dc, ch 2, 3 dc in ch 2 space, skip 3 sts, 4 dc in last st.
Rnd 3- ch 3, 3 dc in same st, skip 3 sts, 3 dc in space, skip 3 sts, 3 dc, ch 2, 3 dc in ch 2 space, skip 3 sts, 3 dc in space, skip 3 sts, 4 dc in last st.
Round 4 ch 1, 2 sc in first st, sc in each st to 2 ch corner, 4 sc in ch 2 corner, sc in each st to the last one, 2 sc in last st.

Squares can be joined however you like. I'm fond of the textural interest of single crocheting them together.
Blank graph 1, with 3 color squares and border.
Blank graph 2 with single color squares and border.
So.. I did more math then I had to. All you have to do is make a square for gauge, measure across the diagonal, and figure out how long/wide you want your shawl to be. If you want a shawl that's 6 feet across, it will be 3 feet long, divide 36 by the number of inches across the diagonal of the square, and you'll know how many squares long to make it. Double that is the number of half squares you'll need. To figure out how many squares total, you can do what I did which is to graph it out and count, or.. and there has to be a simpler way to express this..
X is the number of half squares, Y is the number of squares long.
(X x X)/2 - Y= total number of squares. So in this case..
14 x 14= 196
196/2= 98
98 - 7 = 91.
Whew. Way more work then I needed to do really. Hopefully it comes in handy to *someone*. Thanks to Dot for all her help and for hosting the images.

Oh yeah.. and if anyone makes the rainbow shawl, I want a picture!
 
 
Feeling: amusedamused