When playing chess, the only chess piece which moves around by jumping is a chess piece called knight, why? Is there some kind of special reason why only this piece jumps? The author thinks it has something more to do with mathematics than to simulate an ancient war event.
Chess is closely related to the concept of symmetry. To be a fair game, the positions of chess pieces must be placed in symmetry and so is the layout of a chessboard. Perhaps it is not coincidental that the play field of chess game is all about squares and the Chinese character of "rice field" is also a 2 by 2 square. The chessboard is a tessellation of 8 by 8 squares. Other than circle, no other regular polygons have so many symmetry lines as a square. Circle has infinite symmetry lines and it does not form tessellation so square becomes the battle ground for many board games.
To play a symmetric game the smallest board required is 5 by 5. Chess moves are closely related to geometry translation but with the current traditional way of teaching chess by introducing how each chess piece moves, the relationship between how each piece moves and its geometry meaning has totally lost and perhaps even causes confusion on how chess should be played. For example, the following is a typical description of how each chess piece moves in most chess books.
Chess pieces names and moves
ic che
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Symbol
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Names of chess pieces
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How does it move
(If it is not blocked and is safe to move.)
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q(Q)
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(major piece)
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Up and down
Left and right
Diagonally
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k(K)
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Up and down
Left and right
Diagonally
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r(R)
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(major piece)
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Up and down
Left and right
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n(N)
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(minor piece)
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b(B)
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(minor piece)
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Diagonally
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p
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I believe that the possible movements of each chess piece is originally intended to be a 360 degree circular movement – in any directions with the exception of pawn. So should rook be introduced as moving from side way and top/down or bottom/up? Should knight be introduced as moving in L shape or Y shape?
I think that all pieces should be introduced with the view of moving in 360 degrees, the advantage being the young chess player would then play chess moves also in a 360 degree view which reflects how actually each move should be played.
How the Moves Chess Pieces Should be Taught?
Students should be reminded that in order to look for the "best" move, all possible directions of a chess piece should be considered, thus a chess move actually is moved with the view of 360 degree. This should be the main teaching concept of teaching how each chess piece moves.
For example, take a look at a chess diagram, if a chess piece is placed at c3, how many ways can this chess piece reach out to the side of a square to form a shape of inner circle (inscribed circle c2, b2, e4, d4) or outer circle (circumscribed circle c1, a3, e5, e3)? Depending how points are connected, a shape of square could also be formed.
The first "easy" way would be to move top-down or bottom-up and left-right or right-left, from c3 so as to reach the limit of a square and an inner circle is born and thus the move of rook is born. The motion of its move is called translation or slide. Connect the 4 out reached points with 4 straight lines, the shape is actually a square; but with contour curve then it forms a circle.
The second way of moving to the outer limit of a square and form a circle is to move in the directions of two main diagonals, thus an outer circle is produced and the movements of a bishop is born. Arguably, the four points also make a shape of a square. This motion from c3 to each of the 4 diagonal points is also a double-slide. The bishop can view in 360 degrees.
Combine the above two ways of rook and bishop moving, we have the most powerful move in all chess pieces that is a queen. King can only move in one square in each move and follows the moves of a queen.
In a 5 by 5 chessboard, we notice that all chess squares on each of 4 sides are covered by the moves of rook and bishop except a2, a4, b1, c5, d1, d5, e2, e4, so from a game point of attacking or defending view, this is a problem – there are 8 squares which are not covered. This is the reason of the birth of another chess piece called knight which covers the 8 squares by jumping to those 8 squares because it does not move by following the same moves of rook or bishop to reach the 8 squares. This perhaps is the reason why knight jumps since knight does not trace any squares in one straight line to reach any one of those eight unreachable squares.
By using the moves of up/down, left-/right, diagonals, and diagonal jump, every square on a 5 by 5 chessboard is completely covered from c3.
Summary
By introducing the moves with a view of a circle from one starting square, students could get the sense of how each piece moves and also understands deeply how each move should be made (played) – checking in circular motion of 360 degrees view of course. Further, how each chess piece's move linked to geometry transformation is also introduced to students in a sensible way.
This geometric view of teaching chess movement in 360-degree to form a complete square is much clearer than introducing knight moves in L shape and it also explains why knight jumps – to defend or attack 8 squares where all other chess pieces are not able to achieve.
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