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

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

(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

$(x\_1,y\_1)$ resp.

$(x\_2,y\_2)$, this becomes

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

This concept is named after Pafnuty Chebyshev. In

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

## See also

- Distance
- Lp space
- Uniform norm
- Manhattan distance