[dragonwriter]

> As promised in a sibling comment I would work it out on paper. By my path, using the 7/4 approximation for sqrt(3), the ratio between X and Y directions is 12:21

Well, yes, 4:7 is 12:21.

But I think 4:7 is a lot easier to do in your head than 12:21 (3:5 is a little easier, at the expense of being less accurate); not sure why you did all that work to make it more complicated when you started with a fraction that gave you the ratio in its simplest form.