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

$D\_\{\backslash rm\; Chess\}\; =\; \backslash max\_i(|p\_i\; -\; q\_i|)\; =\; \backslash lim\_\{k\; \backslash to\; \backslash infty\}\; \backslash bigg(\; \backslash sum\_\{i=1\}^n\; \backslash left|\; p\_i\; -\; q\_i\; \backslash right|^k\; \backslash bigg)^\{1/k\}$.

(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

$D\_\{\backslash rm\; Chess\}\; =\; \backslash max\; \backslash left\; (\; \backslash left\; |\; x\_2\; -\; x\_1\; \backslash right\; |\; ,\; \backslash left\; |\; y\_2\; -\; y\_1\; \backslash right\; |\; \backslash right\; )\; .$

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.

See also

• Distance
• Lp space
• Uniform norm
• Manhattan distance

Metric geometry | Chess

Distanza di Chebyshev