##### Wiktionary

**taxicab geometry**

n. (context geometry English) A non-Euclidean geometry in which the distance between two points is the sum of the absolute differences between their corresponding coordinates.

##### Wikipedia

**Taxicab geometry**

**Taxicab geometry**, considered by Hermann Minkowski in 19th-century Germany, is a form of geometry in which the usual distance function of metric or 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** or

**ℓ 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 names allude to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two intersections in the borough to have length equal to the intersections' distance in taxicab geometry.