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Created page with "'''Home * Chess * Chessboard''' FILE:duchamphomageToCaissa.jpg|border|right|thumb|307px|link=http://www.imj.org.il/imagine/collections/item.asp?itemNum=19..."
'''[[Main Page|Home]] * [[Chess]] * Chessboard'''
[[FILE:duchamphomageToCaissa.jpg|border|right|thumb|307px|link=http://www.imj.org.il/imagine/collections/item.asp?itemNum=194326| [[Arts#Duchamp|Marcel Duchamp]] - Homage to Caissa, 1965 <ref>[http://www.imj.org.il/en/collections/194326?itemNum=194326 Homage to Caissa (Hommage à Caissa) | מוזיאון ישראל, ירושלים], [https://en.wikipedia.org/wiki/Israel_Museum Israel Museum]</ref> ]]
The '''Chessboard''' is the playing ground for the [[Chess Game|game of chess]] and its up to 16 white and black [[Pieces|pieces]] each. It consists of [https://en.wikipedia.org/wiki/64_%28number%29 64] [[Squares|squares]], eight rows, called [[Ranks|ranks]], times eight columns, called [[Files|files]]. The squares are alternating dichromatic (light or white, and dark or black squares) on ranks as well on files. Ranks are labeled from '1' to '8', the files from 'A' to 'H' (or with lower case letters 'a' to 'h'), so that each square can be uniquely addressed via concatenated file- and rank labels. The lower left square with the "Address" 'a1' is dark. The [[Diagonals|diagonals]] are the north-east directed, distinguished from the [[Anti-Diagonals|anti-diagonals]] in north-east directions.
Inside a chess program, the chessboard and its piece placement as [[Chess Position|chess position]] is subject of the [[Board Representation|board representation]].
<span id="FourFoldSymmetry"></span>
=Fourfold Symmetry=
The chessboard is fourfold [https://en.wikipedia.org/wiki/Symmetry symmetrical] with respect to rotation about an axis, based on the [https://en.wikipedia.org/wiki/Reflection_symmetry reflection symmetry] of a square ''(not square of a chessboard but the whole board here)''. The four axis are the vertical line between the two center-files 'D' and 'E', the horizontal line between the 4th and 5th rank, and the main-diagonal and main-anti-diagonal. The orthogonal symmetrical squares have different, the diagonal symmetrical squares have same [[Color of a Square|square-colors]].
=See also=
* [[2D Graphics Board]]
* [[3D Graphics Board]]
* [[Squares]]
* [[Ranks]]
* [[Files]]
* [[Diagonals]]
* [[Anti-Diagonals]]
* [[Board Representation]]
* [[Flipping Mirroring and Rotating]]
* [[Pieces]]
* [[Sensory Board]]
=Publications=
* [[Martin Gardner]] ('''1973'''). ''Mathematical Games: How to Turn a Chessboard into a Computer to Calculate with Negabinary Numbers''. [[Scientific American]], Vol. 228, No. 4 <ref>[https://en.wikipedia.org/wiki/Negative_base Negative base from Wikipedia]</ref>
* [[Mathematician#JHAhrens|Joachim H. Ahrens]] ('''1981'''). ''Paving the Chessboard''. [https://en.wikipedia.org/wiki/Journal_of_Combinatorial_Theory Journal of Combinatorial Theory, Series A], Vol. 31, No. 3
* [[Noam Elkies]] ('''2002'''). ''Higher Numbers in pawn endgames on large chessboards''. [http://library.msri.org/books/Book42/ More Games of No Chance] edited by [[Richard J. Nowakowski]]
=External Links=
* [https://en.wikipedia.org/wiki/Chessboard Chessboard from Wikipedia]
* [https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem Wheat and chessboard problem]
* [http://en.chessbase.com/post/a-mathematical-cheboard-paradox A Mathematical Chessboard Paradox] by [[Christian Hesse]], [[ChessBase|ChessBase News]], March 24, 2009
=References=
<references />
'''[[Chess|Up one Level]]'''
[[FILE:duchamphomageToCaissa.jpg|border|right|thumb|307px|link=http://www.imj.org.il/imagine/collections/item.asp?itemNum=194326| [[Arts#Duchamp|Marcel Duchamp]] - Homage to Caissa, 1965 <ref>[http://www.imj.org.il/en/collections/194326?itemNum=194326 Homage to Caissa (Hommage à Caissa) | מוזיאון ישראל, ירושלים], [https://en.wikipedia.org/wiki/Israel_Museum Israel Museum]</ref> ]]
The '''Chessboard''' is the playing ground for the [[Chess Game|game of chess]] and its up to 16 white and black [[Pieces|pieces]] each. It consists of [https://en.wikipedia.org/wiki/64_%28number%29 64] [[Squares|squares]], eight rows, called [[Ranks|ranks]], times eight columns, called [[Files|files]]. The squares are alternating dichromatic (light or white, and dark or black squares) on ranks as well on files. Ranks are labeled from '1' to '8', the files from 'A' to 'H' (or with lower case letters 'a' to 'h'), so that each square can be uniquely addressed via concatenated file- and rank labels. The lower left square with the "Address" 'a1' is dark. The [[Diagonals|diagonals]] are the north-east directed, distinguished from the [[Anti-Diagonals|anti-diagonals]] in north-east directions.
Inside a chess program, the chessboard and its piece placement as [[Chess Position|chess position]] is subject of the [[Board Representation|board representation]].
<span id="FourFoldSymmetry"></span>
=Fourfold Symmetry=
The chessboard is fourfold [https://en.wikipedia.org/wiki/Symmetry symmetrical] with respect to rotation about an axis, based on the [https://en.wikipedia.org/wiki/Reflection_symmetry reflection symmetry] of a square ''(not square of a chessboard but the whole board here)''. The four axis are the vertical line between the two center-files 'D' and 'E', the horizontal line between the 4th and 5th rank, and the main-diagonal and main-anti-diagonal. The orthogonal symmetrical squares have different, the diagonal symmetrical squares have same [[Color of a Square|square-colors]].
=See also=
* [[2D Graphics Board]]
* [[3D Graphics Board]]
* [[Squares]]
* [[Ranks]]
* [[Files]]
* [[Diagonals]]
* [[Anti-Diagonals]]
* [[Board Representation]]
* [[Flipping Mirroring and Rotating]]
* [[Pieces]]
* [[Sensory Board]]
=Publications=
* [[Martin Gardner]] ('''1973'''). ''Mathematical Games: How to Turn a Chessboard into a Computer to Calculate with Negabinary Numbers''. [[Scientific American]], Vol. 228, No. 4 <ref>[https://en.wikipedia.org/wiki/Negative_base Negative base from Wikipedia]</ref>
* [[Mathematician#JHAhrens|Joachim H. Ahrens]] ('''1981'''). ''Paving the Chessboard''. [https://en.wikipedia.org/wiki/Journal_of_Combinatorial_Theory Journal of Combinatorial Theory, Series A], Vol. 31, No. 3
* [[Noam Elkies]] ('''2002'''). ''Higher Numbers in pawn endgames on large chessboards''. [http://library.msri.org/books/Book42/ More Games of No Chance] edited by [[Richard J. Nowakowski]]
=External Links=
* [https://en.wikipedia.org/wiki/Chessboard Chessboard from Wikipedia]
* [https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem Wheat and chessboard problem]
* [http://en.chessbase.com/post/a-mathematical-cheboard-paradox A Mathematical Chessboard Paradox] by [[Christian Hesse]], [[ChessBase|ChessBase News]], March 24, 2009
=References=
<references />
'''[[Chess|Up one Level]]'''
