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Chebyshev distance

In mathematics, the Chebyshev distance, also known as chessboard distance, between two points p and q in Euclidean space with standard coordinates pi and qi respectively is
$D_\left\{Chess\right\} = max_i\left(|p_i - q_i|\right) = lim_\left\{k to infty\right\} left\left( sum_\left\{i=1\right\}^n left| p_i - q_i right|^k right\right)^\left\{1/k\right\}$.

(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$\left(x_1,y_1\right)$ resp. $\left(x_2,y_2\right)$, this becomes
$D_\left\{Chess\right\} = max left \left( left | x_2 - x_1 right | , left | y_2 - y_1 right | right \right) .$

This concept is named after Pafnuty Chebyshev. In chess, the distance between squares, in terms of moves necessary for a king or queen, is given by the Chebyshev distance, hence the second name.