random observation: 17/12 is just slightly over sqrt(2), and 24/17 is just as close but slightly under instead. there's an absolute error of 0.00245 in both cases, and both are ~6 times more accurate than a simple 14/10.
something interesting is that, if you are gonna use x/17 for coordinates, 255/17 is exactly 15 and 65535/17 is exactly 3855. seems like this works for any 2**(8*Z)-1