One thing chess teachers neglect to mention about “the rule of the square”

When chess teachers and chess authors begin talking about pawn endings — the most important kind of endgames to know — they start with “the rule of the square”, a handy device for determining whether one pawn can promote without the help of its king.

If you imagine drawing a diagonal line from the pawn to the eighth rank, that’s the hypotenuse of “the square”. We always draw a big square to demonstrate:

After drawing a3 -> f8 as the hypotenuse — that is, a3 and f8 are two corners of “the square” — we finish drawing its boundaries:

The “rule of the square” says: If the enemy king cannot enter the square with its move, the pawn can promote without assistance. In this position, the king cannot:

Black to move still can’t reach the square 3…Ke8 4. a6 Kd8 4. a7 Kc8 5. a8=Q+ and White wins.

“The rule of the square” makes it easier to understand this vital position. If Black attacks either pawn, the other advances:

I don’t know if this is a composition (in which case, I apologize to the artist, no doubt an early-1700s Italian), or a position that arose in practice. Probably both.

There’s one thing chess educators neglect to mention about “the rule of the square”, because 1) when we draw the square in the first example, the square is too broad; and 2) we’ve forgotten what it’s like to be new at this: Which way do you draw the square?

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