The taxicab metric, also called the taxicab distance, rectilinear distance, city block distance, or Manhattan distance, is the metric of
the Euclidean plane defined by
for all points and . This number is equal to the length of all paths
connecting
and
along horizontal and vertical segments, without ever going back, like those described
by a car moving in a lattice-like street pattern.
and 
. This number is equal to the length of all paths
connecting 
and 
along horizontal and vertical segments, without ever going back, like those described
by a car moving in a lattice-like street pattern.
