Article - A New Chess Set for Teaching Mathematical Chess

8/6/2019 Article - A New Chess Set for Teaching Mathematical Chess

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A New Chess Set for Teaching Mathematical Chess

Frank Ho

Teacher at Ho Math and Chess Learning Centre, www.mathandchess.com

If one thinks that chess game is made of warriors or commanders and kings and queens

battling in the field then this notion does not really address the reason why chess pieces

move in a pattern-like direction for example, rook moves up and down or left and right

and bishop moves diagonally. Is chess game a reflection of ancient war or is it an

invention based on a mathematical principle? The author believes that chess game is

invented by using the geometry symmetry concept and this conjecture is based on

analyzing the moves of each chess piece and thus concludes that this symmetry property

is how chess was created from a mathematical point of view.

To be a fair game, the positions of chess pieces must be placed in symmetry and so isthe 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. Given fixed parameter, the square gives the largest area. The chessboard is a

tessellation of 8 by 8 squares. There are 4 symmetry lines in each square and these 4

symmetry lines constitute the moves of rook, queen, king, pawn and bishop. It makes

sense that each chess piece moves along the symmetry lines to divide each small square

evenly and fairly. How about knight, why knight is the only piece in all chess pieces,

which jumps?

How chess moves are originated

To play a symmetric game the smallest board required is 5 by 5. I believe that the possible

moves of each chess piece are originally intended to be a 360 degrees of circular movement.

For example, take a look at a chess diagram (See Figure 1.), 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 in

addition to circle.

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 moves of

rook is born. The motion of its move is called translation or slide in geometry. 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

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directions of two main diagonals, thus an outer circle is produced and the moves 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 and this is the birth of a queens move. King can onlymove in one square in each move and follows the moves of a queen.

In a 5 by 5 chessboard (see Figure 1), 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 the central point.

Figure 1 5 by 5 Chessboard

This geometric view of chess moves in 360-degree explains how all chess moves were

originated. The moves directions show clearly relationship between geometry symmetry and

chess.

Discovery the key linking math and chess

I believe that my discovery that the chess moves using symmetry property on a square is the

secret key, which links math and chess. The difficult task when teaching children as young

as kindergartners is it understandably takes considerable more time for such young children

to be familiar with on how each piece should move since the chess figures have no clear

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indication on how each relates to symmetry. Without mastering chess moves, children can

not enjoy the joy of playing chess. Often it even becomes frustrated and discouraged for

some children to pursue further. The main reason that children can not master the moves of

each chess piece quickly is there is no clear relation between chess moves and its chess

figurine. It does not seem to make sense for children that why a Rook would move left-right

and up-down. Based on my discovery, I created a Geometry Chess Symbol (GCS, patent

pending) using the concept of geometry and also a new chess teaching set which is created

based on the Geometry Chess Symbol. The response of using GCS to link math and chess

and the testing this new chess set at Ho Math and Chess are very well received, children

could start to play chess almost immediately right after being pointed out that they just have

to move each piece according the moves marked on each piece.

This incredible chess teaching set just plays like an ordinary 3-D chess set but offers

additional advantage that is the moves of each chess piece are clearly marked on its flat

surface to make chess not only easier to learn but also fun for children. It is a "what you seeis what you move" chess set.

The geometry concepts of lines, line segments, transformations, and intersections are used to

design this revolutionary set. It is a great pattern tool to train children's skills in observation,

orientation, decision, and acting with its turn point in the middle of each chess piece.

Children can picture themselves at the intersection of either lines or line segments and then

mover according to the directions pointed by the arrows or the orientation line segments. All

move directions are in line with instructions of any typical chess book. For example, knight

moves in L shape starting with 2 long squares and then makes a turn and ends in one square

move. No more spills or bumps for small hands when moving pieces. Additional advantagewith this pocket-sized, flat surfaced set is to play Blind Chess, which uses a very simple

move rule and is fun to play (more details on how to play Blind Chess, see the end of this

article.). The GCS I invented and the new chess teaching set is illustrated as follows.

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Figure 2 Geometry Chess Symbol and Ho Math and Chess Teaching Set

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Article - A New Chess Set for Teaching Mathematical Chess