The Chess Board

I dont have the answer to this question.

is there a relationship between the 4 center squares of a board, and the 4 corners?

If you take a center square and it's corresponding corner (d4 and a1, for example), it forms a 4x4 chess board with the proper 'white on the right.' 

If you fold the four center squares in half diagonally, you get two triangles and a diamond of opposite colors. If you fold them in half vertically or horizontally, you get a grey blob. :(  (The same would apply for the whole chess board, but on a larger scale.)

A white pawn on e4 or d4 can reach either a8 or h8, but a white pawn on e5 can no longer reach a8, and a white pawn on d5 can no longer reach h8.

There are lots of other strange things we could make up. Are you getting at something in particular?

None of those squares are protected by any peice in the starting position?

right.. i just thought of it. sorry, please dont feel compelled to solve it.

Thank you!

http://www.youtube.com/watch?v=RjibUMZlZX8&feature=related

The real question is whether there's any way to get those six minutes of my life back.

i doubt it... i think i am getting close to solving this one.

Well, the only thing that video triggered for me that might apply to the chess board is that if you similarly number the squares of the chess board the sum of the numbers on the four corners (1+8+57+64=130) is the same as the sum of the numbers on the center squares (28+29+36+37=130).  This is actually true of any  four squares that form a larger square the the corners on those two diagonals.  The video itself was nonsense though.

The problem is that this isn't something that's an attribute of the chess board, but rather of any sequential NxN array of numbers.  The coordinates of a chess board aren't even referenced in this way....

thank you for sharing that info with me.. interesting..

how about this to think about.. the relationship... well if you were to set a number of 1 or 8 starting in any diagonal no matter what point and number you begin with the center squares will always be 4... 4+4+4+4

we could say that the center is a microcosm of the board. the 4 center squares, with the 4 corners.

this leads us to another number which is the number 16.

if you were to add 4 4 4 4 in the center that gives you 16.

if you were to devide the board in 4 that gives you 16 squares in each direction

if you devide the board in any direction or form you get 16 squares.

there are 16 pieces for white, and 16 pieces for black.

the last thing i could think of, which is one of the first i did when thinking baout this, was that if you imagine the chessboard being lifted by the center squares, you get a shape. i dont know the name of that shape.

interesting?!

The 4/16/64 relationship happens to work out because all are powers of two.  the board is 8x8 (8 = 2³) so this should really come as no surprise.  Pure coincidence.

I don't really follow you on the shape that results from picking the board up by the center four squares though -- assuming the squares themselves are rigid, depending the relative rigidity of the vertices the board will fold one of two ways:  Either leaving the d and e files facing skyward or the 4th and 5th ranks.

if you control the d5 square as white does that mean you could gain an initiative on the queen side? if you gain control of the e5 square as whites does that mean you could own the kingside!?!?!?!

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I specialize in useless information.

this is too advanced. i agree.

     There are a couple of lessons in Chess Mentor involving the concept of
"Corresponding Squares" which are fascinating, although I do not fully grasp
the concept yet. 
     Perhaps these center squares correspond in a way with the corner squares
in a way nobody has solved yet, and this is why computers are now so good at
chess.
     In one of my blogs I wrote about the idea of "Visualizing the chessboard as
a circle instead of a square", something I have been experimenting with now.
     Perhaps there is a paradox, by controlling the d5 square white gets an
initiative on the kingside, not the queenside, and we just don't see why yet.
     Since computers are doing so well at chess now it seems logical that humans
have much to learn about this mysterious enigma known as chess.

This question is either very, very deep or completely pointless. I haven't decided which one yet.

I know of a relationship between the 4 center squares and the 4 corners.  If you arrange knights such that they form their own squares, only one center square and one corner square may be occupied.

thats beautiful ;)

corresponding sqaures... difficult!