A queen on d4 attacks twenty-seven squares. The eight nearest squares she cannot touch are b3, b5, c2, c6, e2, e6, f3 and f5, and those are exactly the eight a knight jumps to. That is not a coincidence: the Laws define the knight’s move as a hop to the nearest squares that are not on the same rank, file or diagonal, which is to say the nearest squares no queen can reach.
Rook plus bishop, and nothing else
Article 3.4 gives the queen her powers in a single sentence: any number of squares along the file, rank or diagonal on which she stands. Combine a rook and a bishop and you have built her. There is no clause about jumping and no clause about the L.
She also cannot move through anything in her way, which the knight can. So the two pieces overlap in nothing at all, and that is why queen and knight work so well together in an attack while queen and bishop tend to shout down the same diagonal.
The piece that would do both
It exists, just not here. Chess problemists call a queen plus knight an amazon, and it turns up in the old handicap game Maharajah and the Sepoys, where one player has a single super-piece against a full set. On an 8x8 board the thing is absurd: from d4 it would hit thirty-five squares, more than half the board.
Why a knight is the queen’s worst enemy
Because the two move sets never overlap, a knight attacking a queen is never attacked by her.
g Nine points running from three, every time. This is the engine behind the knight fork, and it is why my first lesson with any new junior is a board full of forks: a knight that attacks the king and the queen at once wins the queen outright, since the check must be answered and the knight can never be shooed away by the piece it is attacking.
If you want the queen’s actual move set square by square, that is over on how the queen moves. If you want to know why the knight is shaped the way it is, the L has a history.