Granny Square Shawl Math

I've been considering a granny square rainbow shawl, and found some notes and sketches from 2008 that I'd completely forgotten about.

If you want to design a triangle shawl using granny squares, you start by deciding how long you want the shawl to be or how wide. If you want a shawl 3 feet long, it will be 6 feet wide, if you want one 7 feet wide, it will be 3.5 feet long. Fairly simple, the length of a right angle triangle shawl is half of the hypotenuse.
Shown on this square, you see the bisection for the hypotenuse and that triangle is bisected again to show length.

I swatched a square with 3 rounds of color and measured it across the diagonal. The square I measured is 3.5 inches approximately across the straight edge. Across the diagonal, it's 5 inches.

You find the number of the of the half squares across the top by dividing. hypotenuse/diagonal of the squares or 72/5=14.4- rounding down because I plan to do a couple rows of border, that's 14 half squares. Since we know the length is half of the hypotenuse, it's 7 full squares down.

For total number of squares, you take the 14 you figured out above, and multiply that by itself to find number of squares in a square.
14x14=196
Divide that in half for the half square.
196/2=98

Since 14 squares are half squares, divide that number by 2 for the number of whole squares they represent. Then subtract that from the number of whole squares figured above.
98- 7= 91

So, for the shawl I have in mind, it will be 91 whole squares, and 14 half squares. Now it's time to make my graph. Click on the image for a larger version.

Then it's just coloring it in, and counting the number of squares in each colorway to know how many squares  and half squares of each to make.Click on the image for a larger version.

The squares I swatched have a single crochet border that I plan to do in black, then join the squares with black single crochet for a stained glass effect.

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.

If you want to do it in single color squares, here's a graph for that.

So now I need to get the yarn!