User:Simures/Move of chess piece

The move of a chess piece is a method of movement of chess pieces, studied from the point of view of certain mathematical regularities embedded in it. Chess pieces can be divided into elementary and complex ones. Elementary pieces are pieces whose move fields do not overlap with the move fields of other elementary pieces. The elementary pieces are a rook, bishop, and knight. This is paired pieces. Complex pieces are the queen. This is unpaired piece. The queen's move is a combination of the rook's move and the bishop's move. Therefore, the queen is not an elementary piece.


 * The king and pawn are not considered in this analysis due to the lack of fundamental regularities in their mode of movement.



Rook move
The simplest principle of building a move belongs to the rook. This is a movement through cells with adjacent sides. This is one straight line. If something interferes with direct vertical or horizontal movement, then further movement is stopped. Theoretically, the rook is an «infinite» piece. That is, its line of movement is limited only to the edges of the board and other pieces when these pieces meet on the squares on which the rook moves.



Bishop's move
The principle of constructing the bishop's move is more complicated. It moves through the cells that touch each other with corners. This is one straight oblique line. If something interferes with the direct diagonal movement, then further movement stops.



Principle of «infinity»
Theoretically, the bishop is also an «infinite» piece, just like the rook. That is, its line of movement is limited only to the edges of the board and other pieces, if these pieces meet on the squares on which the bishop moves.



Rose of the directions of the moves
This drawing is a combination of the rook and bishop move lines from one point. Rook - black lines. Elephant -- green lines. The lines are neither partially nor completely superimposed on each other. Thus, it turns out that the bishop sort of seeps through the cells of the rook's move.



Knight's move
The most difficult principle of building a move belongs to the knight. This is the movement to the cage, which is counted by the letter L. The horse moves in its own unique straight direction. There is no other nearest field for his unique direction, except only on the second square, so it would be quite correct to say about the horse that he goes to his nearest available field in this direction. In its unique equine direction, the classic horse makes only one jump.



Principle of «infinity»
However, purely theoretically, it is easy to imagine such an abstract infinite knight, which, just like a bishop, or also like a rook, jumps along its inclined straight line, from edge to edge in one move, if there is no other figure standing strictly on the square along which this infinite knight jumps. It can be assumed that in practice in chess such an infinite knight is not used because of the disproportionality of its "agility", the speed of movement, and the small size of the board.



Rose of the directions of the moves
This drawing shows combining the lines of the rook, bishop, and knight into one point. Rook - black lines. Elephant - green lines. Horse - blue lines. These lines do not overlap either partially or completely. The knight seeps in its unique straight line between the squares of the rook and bishop moves.



Archer's move
Extrapolating the properties described above, we can imagine what the move of the fourth elementary figure should theoretically look like. Let's call this theoretical figure the archer. And we will use the image of a drawn bow as the icon. The archer jumps on the cells of the third square from the location of the figure, but only on those cells that are not beaten by the bishop and rook. In its unique direction, the archer, as well as an ordinary horse, makes only one jump per turn.

In this analysis, it would be a mistake to divide the archer into two elementary figures of the third cell: one moves "3-1", the other moves "3-2", that is, one is closer to the move of the rook, and the other is closer to the diagonal. The power of each such split piece will be less than half that of a full archer. Such a split into two variants of figures will be incorrect. Since the previous figure, the knight, leaks between all the previous directions without exception, therefore the next figure, the archer, must also follow this principle: divide all the previous angles without exception.



Rose of the directions of the moves
This drawing shows combining the lines of a rook, bishop, knight, and archer into one point. Archer -- purple lines. The lines do not overlap either partially or completely. The archer, as well as the knight, seeps along its unique straight line between the cells of all the previous elementary pieces. The archer's line divides all the previous corners without exception.



Sagittarius move
Continuing the extrapolation, we find the move of the next fifth elementary figure. Let's call this theoretical figure Sagittarius. We will use an image of a wheel or a target as an icon. Sagittarius jumps on the cells of the fourth square from the location of the figure, only on those cells that are opposite in color. That is, if Sagittarius stands on a black square, then he attacks all the white cells of the fourth square from him. If Sagittarius is standing on a white square, then he attacks, respectively, all the black cells of the fourth square from him. In its own unique direction, Sagittarius, as well as an ordinary horse, makes only one jump.