• 107328  Infos

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_{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