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Chessboard


Chessboard

An official chessboard is an 8×8 board containing 64 equal squares alternating between light and dark, on which the game of chess is played (FIDE 2023, Article 2.1). An 8×8 checkerboard can serve as a chessboard. In chess, the board is oriented with a light square at each player's near right corner.

It is impossible to cover a chessboard from which two opposite corners have been removed with dominoes.

Checker
InverseChecker

The above plot shows a chessboard centered at (0, 0) and its inverse about a small circle also centered at (0, 0) (Gardner 1984, pp. 244-245; Dixon 1991).

Chessboard reflected in a sphere

The illustration above shows an infinite chessboard reflected in a sphere.


See also

Checkerboard, Checkers, Chess, Circular Chessboard, Domino, Gomory's Theorem, Inversion, Kings Problem, Knight Graph, Knights Problem, Queens Problem, Rolling Polyhedron, Rooks Problem, Wheat and Chessboard Problem

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References

Dixon, R. "Inverse Points and Mid-Circles." §1.6 in Mathographics. New York: Dover, pp. 62-73, 1991.FIDE. "FIDE Laws of Chess Taking Effect from 1 January 2023." 2023. https://handbook.fide.com/chapter/e012023.Kuiper, H. "Chessboard Deformation" and "Minimal Art by Hans Kuiper: 3D Minimal Art Sculpture Magic Cube II." https://home.hccnet.nl/jc.kuiper/minimal/rotonde.html and https://home.hccnet.nl/jc.kuiper/minimal/3dchess.htm.Pappas, T. "The Checkerboard." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 136 and 232, 1989.Pegg, E. Jr. "Math Games: Chessboard Tasks." Apr. 11, 2005. https://www.mathpuzzle.com/MAA/36-Chessboard%20Tasks/mathgames_04_11_05.html.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 29-30, 1999.Watkins, J. Across the Board: The Mathematics of Chessboard Problems. Princeton, NJ: Princeton University Press, 2004.

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Chessboard

Cite this as:

Weisstein, Eric W. "Chessboard." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Chessboard.html

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