Speaking of Griffiths’ book in the last post prompted me to pull it out and thumb through it; one of the first positions I stopped to examine was the famous “Fahrni Position” under triangulation.
Triangulation is used to put one's opponent in zugzwang by returning to the initial position in such a way that one's opponent is then forced to move first when it is a disadvantage for that player to move. This because he must abandon a blockade and let the other player penetrate his position.
Triangulation occurs most commonly with only kings and pawns when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares.
An example of triangulation is from Fahrni vs. Alapin below. The details of when and where the game was played or if was an actual game position is unknown. It is believed to have been played between 1909 and 1917, possibly in Munich since the two players met in a match (won by Fahrni +3 -0 =1) there in 1909. In Fahrni’s book Das Endspiel im Schach he just quoted it as "From a game Fahrni-Alapin".
What’s weird is that the same position could have occurred in Paul Fiebig vs. Savielly Tartakower in the Barmen Main B tournament in 1905 but White missed the win and only drew because he did not know about triangulation!
One valuable point Griffiths emphasizes is that in defending these types of positions, it is very important that the defender keeps his Pawn as far back as possible since it is less exposed to attack. For example, in the starting position, if Black’s Pawn were on a7 the game would be drawn regardless of who was to move. Also, it is important in any Pawn ending to have as many spare pawn moves as possible because there are many examples where the player who first runs out of pawn moves finds himself in Zugzwang.