An official chessboard is an 
board containing squares
alternating in color between olive green and buff (where "buff" is a color
variously defined as a moderate orange yellow or a light to moderate yellow) on which
the game of chess is played. The checkerboard
is identical to the chessboard, and in both cases, the squares are referred to as
"black" and "white." In chess (as in checkers), the board is
oriented so that each player has a black square on his left.
It is impossible to cover a chessboard from which two opposite corners have been removed with dominoes.
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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).
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, Knights Problem, Knight Graph, 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.Kuiper, H. "Chessboard Deformation" and "Minimal Art by Hans Kuiper: 3D Minimal Art Sculpture Magic Cube II." http://home.hccnet.nl/jc.kuiper/minimal/rotonde.html and http://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. http://www.maa.org/editorial/mathgames/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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Cite this as:
Weisstein, Eric W. "Chessboard." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Chessboard.html