This article is about the distance in finite-dimensional spaces. For the function space norm and metric, see uniform norm.
a
b
c
d
e
f
g
h
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
a
b
c
d
e
f
g
h
The discrete Chebyshev distance between two spaces on a chessboard gives the minimum number of moves a 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∞ metric[1] is a metric defined on a real coordinate space where the distance between two points is the greatest of their differences along any coordinate dimension.[2] 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 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.[3] For example, the Chebyshev distance between f6 and e2 equals 4.
^Cyrus. D. Cantrell (2000). Modern Mathematical Methods for Physicists and Engineers. Cambridge University Press. ISBN 0-521-59827-3.
^Abello, James M.; Pardalos, Panos M.; Resende, Mauricio G. C., eds. (2002). Handbook of Massive Data Sets. Springer. ISBN 1-4020-0489-3.
^David M. J. Tax; Robert Duin; Dick De Ridder (2004). Classification, Parameter Estimation and State Estimation: An Engineering Approach Using MATLAB. John Wiley and Sons. ISBN 0-470-09013-8.
and 25 Related for: Chebyshev distance information
mathematics, Chebyshevdistance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a real coordinate space where the distance between...
Euclidean distance, taxicab distance, and Chebyshevdistance. For points on surfaces in three dimensions, the Euclidean distance should be distinguished from...
limiting case of p {\displaystyle p} reaching infinity, we obtain the Chebyshevdistance: lim p → ∞ ( ∑ i = 1 n | x i − y i | p ) 1 p = max i = 1 n | x i −...
the Chebyshevdistance (L∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshevdistance can be...
get between those two points. Chessboard distance, formalized as Chebyshevdistance, is the minimum number of moves a king must make on a chessboard in...
block distance or Manhattan distance. Chebyshevdistance There are several algorithms to compute the distance transform for these different distance metrics...
of the article. The maximum, L ∞ {\displaystyle L^{\infty }} , or Chebyshevdistance is defined by d ∞ ( ( x 1 , y 1 ) , ( x 2 , y 2 ) ) = max { | x 2...
|f(s)|:s\in S\,\right\}.} This norm is also called the supremum norm, the Chebyshev norm, the infinity norm, or, when the supremum is in fact the maximum...
of radius 1 (using this distance) is the von Neumann neighborhood of its centre. A circle of radius r for the Chebyshevdistance (L∞ metric) on a plane...
Moore neighbourhood of a cell is the cell itself and the cells at a Chebyshevdistance of 1. The concept can be extended to higher dimensions, for example...
are of the same angle, either break ties by increasing distance (Manhattan or Chebyshevdistance may be used instead of Euclidean for easier computation...
Euclidean distance, Manhattan distance, Minkowski distance, and Chebyshevdistance. The Euclidean distance formula is used to find the distance between...
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this...
In kinematics, the Chebyshev Lambda Linkage is a four-bar linkage that converts rotational motion to approximate straight-line motion with approximate...
statistics and number theory, author of the Chebyshev's inequality, Chebyshevdistance, Chebyshev function, Chebyshev equation etc. Sergei Chernikov, significant...
dimension of a d {\displaystyle d} -dimensional vector space with the Chebyshevdistance ( L ∞ {\displaystyle L^{\infty }} norm) is 2 d {\displaystyle 2^{d}}...
unwanted deviation, rather than the sum of deviations. This utilises the Chebyshevdistance metric. A major strength of goal programming is its simplicity and...
reached using simpler calculations – for example, using Chebyshevdistance over Euclidean distance in two-dimensional space.) As the value of the heuristic...
norm, including the euclidean metric, the taxicab metric, and the Chebyshevdistance, are equivalent. The continuity of a function is preserved if either...
x_{i+m-1}\}}} and the distance function d [ X m ( i ) , X m ( j ) ] {\displaystyle d[X_{m}(i),X_{m}(j)]} (i≠j) is to be the Chebyshevdistance (but it could be...
In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion. It was invented by the 19th-century...
in taxicab geometry, and a cube is a sphere in geometry using the Chebyshevdistance. The geometry of the sphere was studied by the Greeks. Euclid's Elements...
that have the same nearest distance to x. In the special case in which pM is single-valued, the set M is called a Chebyshev set. As an example, if (X,d)...
statistics and number theory, author of the Chebyshev's inequality, Chebyshevdistance, Chebyshev function, Chebyshev equation Boris Delaunay, inventor of Delaunay...
Global Information
