Chessboard

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.

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.

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.