To find rules for the number of squares a queen can attack from a point on a chess board and the minimum and maximum squares a queen can attack from a given rectangular chessboard.

The queen on a chess board is the most powerful piece. From one square, the queen can attack anywhere around it in a straight line without skipping squares (as the diagram illustrates on the right). The squares where the arrow cuts through are the ones the queen can attack and the queen can carry on attacking in those straight lines. However the queen can't jump squares to attack, these squares are marked with an x. …

…are left with the formula: n+2n-3=3n-3 .*. 3n-3=3n-3 And so I've proved a square is a special rectangle. From my extensional investigation, I have come to realise and prove how a square is a special rectangle with many more qualities. It has four lines of symmetry, all four sides are equal, and it has a rotational symmetry of 4. Note: Pictures are missing as I couldn't paste them in, sorry. Please dont blatently copy.