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Stepping into the Square

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dragon60
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         Stepping into the Square of the Pawn                                 

                   

  In this setup, the "square of the pawn" extends from h5 to d1 to d5.  White enters it at d5 immediately.  A visual shortcut is to draw an imaginary diagonal line from the pawn to the back rank--here, h5 to d1.  The d-file then becomes the line White's King must cross.  It does so on the move.  The diagonal containing White's King and the promotion square is the "critical diagonal."  In the diagram it is d5-e4-f3-g2-h1. 
Retreating the King along a critical diagonal can be paramount to an endgame's solution.
The defender uses the path to get back quickly, while the superior side tries to obstruct it.

Play continues:
1. Kd5  h4   2. Ke4  h3   3. Kf3  h2   4. Kg2  h1/Q+   5. Kxh1  Draw