Chessboard distance

In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L_∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev.

It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board. For example, the Chebyshev distance between f6 and e2 equals 4.

The Chebyshev distance between two vectors or points p and q, with standard coordinates ${\displaystyle p_{i}}$ and ${\displaystyle q_{i}}$, respectively, is

This equals the limit of the L_p metrics:

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