[gqcwwjtg]

It exists in a hyperbolic space. So the area reachable in radius r is not r^2, but x^r for some x>1.

It doesn’t violate the triangle inequality, but it does mean that there’s way more than one parallel line through a given point off an initial line. I think that’s Euclid’s axiom.

Intuitively, the mechanics make it easier to run away from groups of enemies, since the angle it would take to follow you is more precise. It also makes it harder to find and return to earlier locations. In fact, to win the game you have to find an “orb of yendor”, then a key spawns 100 tiles away with an arrow helping you find it. The hard part is getting back to the orb once you get the key.