Taxicab geometryTaxicab geometry
, considered by Hermann Minkowski
in the 19th century
, is a form of geometry
in which the usual metric
of Euclidean geometry
is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates. More formally, we can define the Manhattan distance
, also known as the L1-distance
is the distance
between two points measured along axes at right angles. In a plane
) and p2
), the Manhattan distance is:
- , when m = 1.
(One can note that the L2
-distance is the normal Euclidean distance
Manhattan distance is also known as city block distance. It is so named because it is the distance a car would drive in a city laid out in square blocks, like Manhattan (discounting the facts that in Manhattan there are one-way and oblique streets and that real streets only exist at the edges of blocks - there is no 3.14th Avenue). Any route from a corner to another one that is 3 blocks East and 6 blocks North, will cover at least 9 blocks.