taxicab metric

The taxicab metric is a distance function used in mathematics, particularly in topology. It defines the distance between two points in a Euclidean plane as the sum of the absolute differences of their Cartesian coordinates. This means the distance is calculated as if one were traveling along a grid of streets, like a taxi in a city, rather than in a straight line. For two points (x, y) and (z, w), the taxicab distance is |x - z| + |y - w|. This concept is a generalization of the usual distance and is an example of a metric space. The term "taxicab" itself originates from the taximeter, a device used to measure fares in hired vehicles.1234