It's Border Time, or Right Brain and Left Brain Duke It Out with the Pythagorean Theorem

I've got a border.  Much math was invoked.  There were even square roots.

Here's the mockup:

And another view from a bit further back:

And an attempted closeup of the perfect border fabric I found (on sale, no less!)  (It's greener than it looks, but the dark factor is about right.)

That's where the math came in.  I'm running a 1" light border around the patchwork center, then a dark border of width-to-be-determined-through-math, then the on-point nine-patches set with orange triangles, then dark border again (easy math this time), then binding in orange.
The fun started with that inside dark border.  Pythagoras told me that my nine-patches on point measure  4.2526406871192851 inches tall and wide.  (I'm rounding it down to 4.25" just for fun.)  Figuring the size of the completed center plus the 1" light borders, and calculating how many diagonal nine-patches I'd need to cover that distance plus enough for a dark border wasn't all that hard - 15 nine patches across for the top and the bottom, and 18 on the sides (not counting corners) would work just fine.
Except for one thing.  The calculations showed that the vertical inner borders would have to be 3/8" narrower than the horizontal ones.
This is where my right brain and my left brain declared war on each other.
Left Brain was all "Okay, the dark border will be 3/8" wider on the top and the bottom than on the sides.  Two and 3/8" here and two and 3/4" there.  No problem."
And Right Brain was all "NOOOOO!!!  It'll be lopsided.  It'll show and every part of it will look wrong.  It'll be out of balance.  It'll look like robots did it.  No.  Just no."
So then Left Brain was "Oh, stop whining.  We'll just  make the light borders on the top and bottom 3/8" wider - that won't be so obvious.  We were going to use those leftover 1.5" strips, but we can cut some extra strips to finish at 3/8", so that means starting with 7/8" strips.  One border of 1.5" and one at 7/8" will finish to 1 3/8".  Easy peasy."
So then Right Brain comes back with "Red.  The 3/8" borders in red.  So it looks like it's on purpose.  That'll be great.  Yep, red.  Or purple.  No, definitely red."
And Left Brain was "Nope nope nope, that's ridiculous.  Your ideas are stupid."  and Right Brain would have bopped Left Brain right on the nose at that point if I hadn't intervened.
"Look, both of you just back down and chill out.  First of all, I'm using 4.25" for my calculations but the actual measurement is 4.2526406871192851 - do you think that .0026406871192851 times 18 might not come back to bite my ass?  And besides, do you honestly think I can sew 18 nine-patches, on point, set with at least 36 bias-y triangles, and actually be so accurate that I'm only going to be off by 3/8 of an inch?"
That shut them up.
So the plan (because I often pretend I have a plan) is to piece all my nine-patches for the borders, and THEN calculate what widths I'll need for the dark borders.
Because I'm an empiricist, not a theoretician.  That whole "If my calculations are correct, this might work" doesn't hold a candle to "Let's just do it and then measure it afterward."



(Whoopee!  There's another fantastic scrap gathering!  Go visit Scraptastic Tuesday at Mrs Sew and Sow's for all kinds of gorgeousness!)