Let's first take a look at simple cases of orthogonally and diagonally moving chess pieces, which are the king, queen, rooks, and bishops. We need somehow to figure out a way to change the position of these chess pieces by using a mathematical rule.
The following diagram shows what it takes to move a chess piece from its current position (say x, y) both orthogonally and diagonally:
If you look at the preceding diagram, x represents the column number and y represents the row number. It is clear that we can represent the orthogonal movements by adding to the current position the items from the tuples ...
