Chebyshev distance

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In mathematics, the Chebyshev distance, also known as chessboard distance, between two points p and q in Euclidean space with standard coordinates p_i and q_i respectively is

[D_ = \max_i(|p_i - q_i|) = \lim_ \bigg( \sum_^n \left| p_i - q_i \right|^k \bigg)^].

(This is in fact a special case of the supremum norm.)

In two dimensions, i.e. plane geometry, if the points p and q have Cartesian coordinates [(x_1,y_1)] and [(x_2,y_2)], this becomes

[D_ = \max \left ( \left | x_2 - x_1 \right | , \left | y_2 - y_1 \right | \right ) .]

This concept 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.

Chebyshev distance

See also