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'''[[Main Page|Home]] * [[Chess]] * [[Tactics]] * Triangulation'''
[[FILE:Gemma Frisius - Driehoeksmeting.jpg|border|right|thumb|[https://en.wikipedia.org/wiki/Gemma_Frisius Gemma Frisius's] 1533 triangulation for mapmaking proposal <ref>[https://en.wikipedia.org/wiki/Triangulation Triangulation from Wikipedia]</ref> ]]
'''Triangulation''' in chess is an [[Endgame|endgame]] related tactic to put the opponent in [[Zugzwang|zugzwang]] by explicitly losing a [[Tempo|tempo]]. Triangulation performs an artificial [[Null Move|null move]], a [[Pieces|piece]] (except [[Pawn|pawn]] and [[Knight|knight]]) uses three moves to return to its [[Origin Square|original square]], while the defending side is not able to do so.
Most often triangulation occurs with the [[King|king]] in [[Pawn Endgame|pawn endings]] to "win" the [[Opposition|opposition]]. [[Queen]]-triangulation is a theme in KQKR, as demonstrated in [https://en.wikipedia.org/wiki/Fran%C3%A7ois-Andr%C3%A9_Danican_Philidor Philidor's] KQKR position <ref>[https://en.wikipedia.org/wiki/Philidor_position#Queen_versus_rook Philidor Position in KQKR from Wikipedia]</ref>, while [[Rook|rook]]-triangulation <ref>[https://en.wikipedia.org/wiki/Triangulation_%28chess%29#Triangulation_with_a_rook Triangulation with a rook from Wikipedia]</ref> is a motive in [[Rook Endgame|rook endgames]], and [[Bishop|bishop]]-triangulation happens rarely in [[Bishop versus Knight|bishop versus knight]] endings <ref>[https://en.wikipedia.org/wiki/Zugzwang#Fischer_versus_Taimanov.2C_fourth_match_game Fischer versus Taimanov, fourth match game from Wikipedia]</ref>. In blocked [[Pawn Endgame|pawn endgames]], triangulation and [[Opposition|opposition]] is incorporated in the general concept of [[Corresponding Squares|corresponding squares]].
Triangulation, like any other zugzwang related motives, requires some care in [[Search|search]] using [[Null Move Pruning|null move pruning]]. Most programs either disable null move pruning completely in such late endgames, or at least perform a [[Null Move Pruning#ZugzwangVerification|verification search]].
=See also=
* [[Corresponding Squares]]
* [[Null Move Pruning]]
* [[Opposition]]
* [[Zugzwang]]
=External Links=
* [https://en.wikipedia.org/wiki/Triangulation_%28chess%29 Triangulation (chess) from Wikipedia]
* [https://en.wikipedia.org/wiki/Triangulation_%28disambiguation%29 Triangulation (disambiguation) from Wikipedia]
* [http://chess-training.blogspot.com/2006/11/corresponding-squares-and-triangulation.html Chess Training: Corresponding Squares and Triangulation]
=References=
<references />
'''[[Tactics|Up one Level]]'''
[[FILE:Gemma Frisius - Driehoeksmeting.jpg|border|right|thumb|[https://en.wikipedia.org/wiki/Gemma_Frisius Gemma Frisius's] 1533 triangulation for mapmaking proposal <ref>[https://en.wikipedia.org/wiki/Triangulation Triangulation from Wikipedia]</ref> ]]
'''Triangulation''' in chess is an [[Endgame|endgame]] related tactic to put the opponent in [[Zugzwang|zugzwang]] by explicitly losing a [[Tempo|tempo]]. Triangulation performs an artificial [[Null Move|null move]], a [[Pieces|piece]] (except [[Pawn|pawn]] and [[Knight|knight]]) uses three moves to return to its [[Origin Square|original square]], while the defending side is not able to do so.
Most often triangulation occurs with the [[King|king]] in [[Pawn Endgame|pawn endings]] to "win" the [[Opposition|opposition]]. [[Queen]]-triangulation is a theme in KQKR, as demonstrated in [https://en.wikipedia.org/wiki/Fran%C3%A7ois-Andr%C3%A9_Danican_Philidor Philidor's] KQKR position <ref>[https://en.wikipedia.org/wiki/Philidor_position#Queen_versus_rook Philidor Position in KQKR from Wikipedia]</ref>, while [[Rook|rook]]-triangulation <ref>[https://en.wikipedia.org/wiki/Triangulation_%28chess%29#Triangulation_with_a_rook Triangulation with a rook from Wikipedia]</ref> is a motive in [[Rook Endgame|rook endgames]], and [[Bishop|bishop]]-triangulation happens rarely in [[Bishop versus Knight|bishop versus knight]] endings <ref>[https://en.wikipedia.org/wiki/Zugzwang#Fischer_versus_Taimanov.2C_fourth_match_game Fischer versus Taimanov, fourth match game from Wikipedia]</ref>. In blocked [[Pawn Endgame|pawn endgames]], triangulation and [[Opposition|opposition]] is incorporated in the general concept of [[Corresponding Squares|corresponding squares]].
Triangulation, like any other zugzwang related motives, requires some care in [[Search|search]] using [[Null Move Pruning|null move pruning]]. Most programs either disable null move pruning completely in such late endgames, or at least perform a [[Null Move Pruning#ZugzwangVerification|verification search]].
=See also=
* [[Corresponding Squares]]
* [[Null Move Pruning]]
* [[Opposition]]
* [[Zugzwang]]
=External Links=
* [https://en.wikipedia.org/wiki/Triangulation_%28chess%29 Triangulation (chess) from Wikipedia]
* [https://en.wikipedia.org/wiki/Triangulation_%28disambiguation%29 Triangulation (disambiguation) from Wikipedia]
* [http://chess-training.blogspot.com/2006/11/corresponding-squares-and-triangulation.html Chess Training: Corresponding Squares and Triangulation]
=References=
<references />
'''[[Tactics|Up one Level]]'''
