After looking at diagonal movement on a square grid, I started wondering how far a figure would need to move before the difference between 3⁄2 and the √2 square root of two became significant. (Simple curiosity here. Nothing more.)
What amount of error is significant? 1⁄2? 1? 3⁄2?
Let’s go with 1. Check my math: (sqrt(2) * x) + 1 = 1.5 * x
It turns out x is about 12. Here’s my check: (1.5 * x) - (sqrt(2) * x); x = 12 which yields a result just a little over 1.
That’s smaller than I was expecting. Though it is still reasonable for most games. A twelve square per turn movement rate will start to get problematic for other reasons.