The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1, y_1), (x_2, y_2)) = |x_1 - x_2 | + |y_1 - y_2 |, for all points P_1(x_1, y_1) and P_2(x_2, y_2). This number is equal to the length of all paths connecting P_1 and P_2 along horizontal and vertical segments, without ever going back, like those described by a car moving in a lattice-like street pattern.
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