Editing Chebyshev distance (section)

{{Short description|Mathematical metric}}
{{About|the distance in finite-dimensional spaces|the function space norm and metric|uniform norm}}
{{Chess diagram small
| tright
| 
|x5|x4|x3|x2|x2|x2|x2|x2
|x5|x4|x3|x2|x1|x1|x1|x2
|x5|x4|x3|x2|x1|kl|x1|x2
|x5|x4|x3|x2|x1|x1|x1|x2
|x5|x4|x3|x2|x2|x2|x2|x2
|x5|x4|x3|x3|x3|x3|x3|x3
|x5|x4|x4|x4|x4|x4|x4|x4
|x5|x5|x5|x5|x5|x5|x5|x5
| The discrete Chebyshev distance between two spaces on a [[chessboard]] gives the minimum number of moves a [[king (chess)|king]] requires to move between them. This is because a king can move diagonally, so that the jumps to cover the smaller distance parallel to a row or column is effectively absorbed into the jumps covering the larger. Above are the Chebyshev distances of each square from the square f6.
}}

In [[mathematics]], '''Chebyshev distance''' (or '''Tchebychev distance'''), '''maximum metric''', or '''L<sub>∞</sub> metric'''<ref>{{cite book | title = Modern Mathematical Methods for Physicists and Engineers | url = https://archive.org/details/modernmathematic0000cant | url-access = registration | author = Cyrus. D. Cantrell | isbn = 0-521-59827-3 | publisher = Cambridge University Press | year = 2000 }}</ref> is a [[Metric (mathematics)|metric]] defined on a [[real coordinate space]] where the [[distance]] between two [[point (geometry)|points]] is the greatest of their differences along any coordinate dimension.<ref>{{cite book
 | editor1-last = Abello | editor1-first = James M.
 | editor2-last = Pardalos | editor2-first = Panos M.
 | editor3-last = Resende | editor3-first = Mauricio G. C. | editor3-link = Mauricio Resende
 | isbn = 1-4020-0489-3
 | publisher = Springer
 | title = Handbook of Massive Data Sets
 | year = 2002}}</ref> It is named after [[Pafnuty Chebyshev]].

It is also known as '''chessboard distance''', since in the game of [[chess]] the minimum number of moves needed by a [[king (chess)|king]] to go from one square on a [[chessboard]] to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board.<ref>{{cite book | title = Classification, Parameter Estimation and State Estimation: An Engineering Approach Using MATLAB |author1=David M. J. Tax |author2=Robert Duin |author3=Dick De Ridder | isbn = 0-470-09013-8 | publisher = John Wiley and Sons | year = 2004}}</ref> For example, the Chebyshev distance between f6 and e2 equals 4.