re: Irrational numbers
The math holds up, but a more practical reason for going all the way east on one road, then all the way north on another (for example) is that you don't waste a lot of time slowing down to turn corners jigging back and forth.
In the real world, the type of road, number of stoplights, and other things makes as big a difference as the distance.
Of course, if you're a sailor, going someplace by tacking back and forth instead of taking the straight route might be second nature.