Chess + Coordinate Plane = Transformation

At one point in my life, I learned chess.  I didn't learn it because I had a burning desire to learn it but my brother decided to learn the game and needed someone to play against.  I didn't care for the game because no one took time to explain one needs to think about the consequences of various moves.  I had no problem with the movement of each piece. because every move could be explained in terms of movement.

Just the other night, I realized chess has so much in common with the coordinate plane.  When my brother taught me chess, he neglected to mention the notation system used in it.  A board is 8 squares by 8 squares or a total of 64 squares.  Assume the chessboard is in quadrant one of the coordinate plane.  The 8 squares along the x-axis are given letters a to h, while the 8 squares lining up along the y-axis are given numbers from one to eight. When you hear someone say "Knight to c3" it means the person is moving his night to the third column along the x axis, then up three units to the third row.  If we were thinking in terms of normal coordinates, we'd say (3,3).

I suspect the use of letters for one coordinate makes it less confusing but this notation system is referred to Algebraic notation.  It is customary to use this system to write down all the moves made during a game so the serious players can go back and review every move, looking for errors and mistakes.  This is the way they improve their playing ability.

Another thing about chess is that all pieces pretty much move in a linear direction.  Some pieces move along a line with a slope of 2 or -2 while others move along a line with a slope of 1 or -1.  Then there are pieces that can move only one square or one jump while others move across the board in one smooth line with a slope of zero or undefined.  Every move can be defined as a transformation.

Chess players use another geometric concept called the "rule of square".  They visualize a square to determine if a pawn will get through the other players defenses.  This has been used since the Middle Ages as a way to make a judgement without using a lot of mathematics.

Furthermore, mathematicians have created two problems  based on chess pieces and a chess board.  One is the Eight Queens problem where people try to place eight queens on a chessboard so that none of the queens threaten each other.  The problem was thought of in 1848 by Max Bezzel in Germany and it wasn't solved until 1972 with the help of computers and lots of work.

Another problem is the Knight's Tour problem where you try to have the knight visit every single square on the board.  This problem is directly related to the Hamiltonian path problem in graph theory.  This problem dates back to Arabic manuscripts from the 9th century.  Mathematicians found several different solutions including Euler which he presented at the 1759 meeting of the Berlin Academy of Sciences.

I love that chess is mathematically related  and I've learned there are several high ranking chess players who are mathematicians.  I wish I'd known more about the chessboard when I first learned chess.  It might have made it easier for me to learn more about it.  Let me now what you think, I'd love to hear.  Have a great day.