The taxicab metric, also called the 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.
