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Help on Magic Squares (geometrical structure of MS in a vector space of pseudomagical squares)
Posted:
Jun 18, 1996 8:28 PM


Hi! I found a base, which helps to create pseudomagic 3x3 Squares (no need, that the numbers have to be 1 .. 9):
x1 x2 x3 1 0 0 0 1 0 0 0 1 ( x4 x5 x6 ) = a*(2/3 1/3 4/3) + b*(1/3 1/3 1/3) + c*(4/3 1/3 2/3) x7 x8 x9 2/3 2/3 1/3 2/3 1/3 2/3 1/3 2/3 2/3
Ergo: The pseudomagic Squares create a 3dimensionalsubroom.
2. I found, that the magic 3x3 squares (with numbers from 1..9) are in a plane:
x1 x2 x3 1 0 1 0 1 1 0 0 1 ( x4 x5 x6 ) = a*(2 0 2) + b*(1 0 1) + 15*(4/3 1/3 2/3) x7 x8 x9 1 0 1 1 1 0 1/3 2/3 2/3
Can I say, that the magic squares are points of a plane lying in a 3dimpseudomagicsquare? What have I to do?
I have to find out, if the nxn magicsquares create a geometrical figure in the vector room, that is built by the pseudomagical nxn squares? (4x4, 5x5)
Do you have any idea, how to generalize from 3x3 to nxn?
TIA Oliver



