Triangulation is deliberately ‘losing a move’: your king takes three moves to return to the same square, so the same position arrives with the opponent to move — and in zugzwang.
Sometimes the only thing standing between you and the win is whose turn it is. If you could just pass, the opponent would be in zugzwang. Triangulation is how you pass: your king walks a little triangle (three squares, three moves) and comes back to where it started.
Because your king has an extra square to waste a move on and the opponent’s doesn’t, the position repeats — but now it’s their move. They’re forced to give ground, lose the opposition, or abandon a key square.
It’s a king trick (a knight can’t do it), and it shows up most in king-and-pawn endgames, often to grab the opposition you couldn’t get directly.
Triangulation works because a king can reach the same square in either two or three moves, changing whose turn it is. A knight always returns to a square in an even number of moves, so it can’t flip the move count.
To put the opponent in zugzwang. Many endgames are won only if it’s the other side’s turn — triangulation is the maneuver that arranges exactly that.
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