Taxicab geometry [SEP] named after
Taxicab geometry
A taxicab geometry is a form of geometry in which the usual distance function or 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 Cartesian coordinates. The taxicab metric is also known as rectilinear distance, L" distance, L" distance or formula_1 norm (see "L" space), snake distance, city block distance, Manhattan distance or Manhattan length, with corresponding variations in the name of the geometry. The latter
length in taxicab geometry is 2"r". Thus, a circle's circumference is 8"r". Thus, the value of a geometric analog to formula_39 is 4 in this geometry. The formula for the unit circle in taxicab geometry is formula_40 in Cartesian coordinates and
in polar coordinates.
A circle of radius 1 (using this distance) is the von Neumann neighborhood of its center.
A circle of radius "r" for the Chebyshev distance (L metric) on a plane is also a square with side length