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'''[[Main Page|Home]] * [[Evaluation]] * [[Game Phases]] * [[Endgame]] * [[Pawn Endgame]] * Corresponding Squares'''
[[FILE:CoSq.jpg.png|right|thumb| 6k1/3p4/3p4/3P4/4P1p1/6P1/8/K7 w - - ]]
'''Corresponding Squares''', also called '''Co-ordinate Squares''' is a concept to analyse pawn endgames. Using [[Retrograde Analysis|retrograde analysis]], [[Zugzwang]] positions and Critical Squares are found. Corresponding Squares Systems were one of the first human attempts of finding formulas and finally solving certain chess positions. This concept is only possible due to the limited mobility in pawn endgames. King-oppositions and Zugzwangs are the main motives arising.
=Theory=
To get an idea, the concept is described using an example position by [https://en.wikipedia.org/wiki/British_Chess_Championship Charles_Dealtry_Locock Charles Dealtry Lockock], 1892 <ref>Position by [https://en.wikipedia.org/wiki/British_Chess_Championship Charles_Dealtry_Locock Charles Dealtry Lockock], 1892, from [https://en.wikipedia.org/wiki/Yuri_Averbakh Yuri Averbakh], [httphttps://delv.wikipedia.org/wiki/Ilja_Lwowitsch_Maiselis I%C4%BCja_Maizelis Ilia Maizelis] ('''1987'''). ''Comprehensive Chess Endings Vol 4: PawnEndings, Cadogan Books 1987''.Cadogan Books</ref> :[[FILE:CoSq.jpg.png|none|border|text-bottom]] 6k1/3p4/3p4/3P4/4P1p1/6P1/8/K7 w - -
==Finding Critical Squares==
==Constructing Corresponding Square System==
[[FILE:CoSq2.png|right|thumb]]
This particular example, where two Corresponding Squares are connected diagonally and there is enough space for a 3x3 square, [https://en.wikipedia.org/wiki/Yuri_Averbakh Averbakh] called the eight-square system. The construction of this Corresponding Square System starts with numbering the first two Corresponding Squares 1 and 2 accordingly. The square connecting the two receives the number 3. The outer squares of the 3x3 field receive the numbers 4 to 8. Further outside the numbering can continue by using the number of a square exactly two squares away either diagonally, horizontally or vertically. The image below should exemplify this process.
==Using the Corresponding Square System==
=Publications=
* [https://en.wikipedia.org/wiki/Vitaly_Halberstadt Vitaly Halberstadt], [[Arts#:Category:Marcel Duchamp|Marcel Duchamp]] ('''1932'''). ''L'opposition et les cases conjuguées sont réconciliées''.
: Paris-Brussels 1932, German Edition 2001 ''[http://www.buecher-nach-isbn.info/3-608/3608500359-Opposition-und-Schwesterfelder-Marcel-Duchamp-Vitali-Halberstadt-3-608-50035-9.html Opposition und Schwesterfelder]'', ISBN 3-932170-35-0
* [[Kenneth W. Church]] ('''1978'''). ''[http://dl.acm.org/citation.cfm?id=67030 Co-ordinate Squares: A Solution to Many Chess Pawn Endgames]''. B.Sc. thesis, [[Massachusetts Institute of Technology]], reprinted 1988 in [[Computer Chess Compendium]]
* [[Karsten Müller]], [https://en.wikipedia.org/wiki/Frank_Lamprecht Frank Lamprecht] ('''2000'''). ''Secrets of Pawn Endings''. [https://en.wikipedia.org/wiki/Everyman_Chess Everyman Chess], ('''2007'''). [http://dev.jeremysilman.com/shop/pc/Secrets-of-Pawn-Endings-p3748.htm re-issue] by [https://en.wikipedia.org/wiki/Gambit_Publications Gambit Publications]
* [[Karsten Müller]] ('''2004'''). ''Endgame Corner - The Mystical Sister Squares'', [http://www.chesscafe.com/text/mueller38.pdf pdf] from [https://en.wikipedia.org/wiki/ChessCafe.com ChessCafe.com]
* [[Eli David|Omid David]], [[Ariel Felner]], [[Nathan S. Netanyahu]] ('''2004'''). ''Blockage Detection in Pawn Endgames''. [[ICGA Journal#27_3|ICGA Journal, Vol. 27, No. 3]]
=Postings=
'''[[Pawn Endgame|Up one level]]'''
[[Category:Marcel Duchamp]]
