Taxicab Geometry

Taxicab geometry, also called Manhattan geometry, is a form of geometry in which the distance between two points is measured as the sum of the absolute differences of their coordinates rather than the straight line distance used in ordinary Euclidean geometry. In two dimensions the taxicab distance between points (x1, y1) and (x2, y2) is the absolute value of x1 minus x2 plus the absolute value of y1 minus y2, matching the distance a taxicab would have to drive along a rectangular street grid, moving only horizontally and vertically. The name was introduced by Karl Menger in 1952 for a geometry exhibit at a Chicago science museum, evoking the island of Manhattan or any city built on a rectangular grid of streets. The same distance is also called the Manhattan distance, city block distance, or L1 distance, and its geometric study developed in the nineteenth century through the work of mathematicians including Hermann Minkowski. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/