Taxicab 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, as the distance between two points measured along axes at right angles. In a plane, the Manhattan distance between the point P1 with coordinates (x1, y1) and the point P2 at (x2, y2) is
| x1 - x2 | + | y1 - y2 | .
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.
Manhattandistance is a measure of the distance between two vertices used in computer go.
A "circle" is defined as the set of all points that have the same distance from a given point.
Fhayashi: Presumably, the name reflects the fact that in modern urban cities with orthogonal streets, regardless of the straight-line distance between two points, the practical distance is the number of block-sides you must transit to get to your destination...
In the case of two locations on Earth, usually the distance along the surface is meant: either " as the crow flies " (along a great circle) or by road, railroad, etc. Distance is sometimes expressed in terms of the time to cover it, for example walking or by car.
Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction.
The distance covered by a vehicle (often recorded by a odometer), person, animal, object, etc. should be distinguished from the distance from starting point to end point, even if latter is taken to mean e.g.
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