Manhattan distance

The Manhattan distance is a different way of measuring distance. It is named after the grid shape of streets in Manhattan. If there are two points,  and , the Manhattan distance between the two points is .

This distance can be imagined as the length needed to move between two points in a grid where you can only move up, down, left or right.

Extension
This definition can be used for three and higher dimensions too.
If there are two vectors,  and , then the manhattan distance between the two points is the absolute value of the difference between all numbers in the vector. Or, in notation:

Category:Mathematical notation