Chebyshev distance
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In mathematics, the Chebyshev distance between two points p and q in Euclidean space with standard coordinates pi and qi respectively is
- .
The Chebyshev distance is in fact a special case of the supremum norm, and is also known as chessboard distance or the L∞ metric. It is an example of an injective metric.
In two dimensions, i.e. plane geometry, if the points p and q have Cartesian coordinates (x1,y1) and (x2,y2), this becomes
The "circle" of radius r in the Chebyshev metric is a square with side length 2r parallel to the coordinate axes. The two dimensional Manhattan distance also has circles in the form of squares, with side length √2r, at an angle of π/4 to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to the planar Manhattan distance. However this equivalence between L1 and L∞ metrics does not generalize to higher dimensions.
The Chebyshev distance is named after Pafnuty Chebyshev. In chess, the distance between squares, in terms of moves necessary for a king, is given by the Chebyshev distance, hence the second name.