Taxicab geometry

• abstract: Taxicab geometry, considered by Hermann Minkowski in 19th century Germany, 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, L1 distance or \ell_1 norm (see Lp space), city block distance, Manhattan distance, or Manhattan length, with corresponding variations in the name of the geometry.

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