05 August 2011

One and a half versus the square root of two

After looking at diagonal movement on a square grid, I started wondering how far a figure would need to move before the difference between 32 and the √2 square root of two became significant. (Simple curiosity here. Nothing more.)

What amount of error is significant? 12? 1? 32?

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.

1 comment:

Aaron E. Steele said...

If you give your typical human a move of 6" per turn, you can minimize any problems