What measures distance?

Answer 1

There are several different metrics. The most common is the Euclidean or Pythagorean distance where if P = (a, b) and Q = (c, d) are two points in the Cartesian plane then the distance between then is sqrt[(a - c)^2 + (b - d)^2)]. Another metric is the Minkovski or taxicab measure, based on a grid structure of roads. Since you cannot travel "cross country", the distance would be |a - c|+ |b - d|.