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Topic: Help on Magic Squares (geometrical structure of MS in a vector space of pseudo-magical squares)
Replies: 0

 PaulAtre Posts: 2 Registered: 12/12/04
Help on Magic Squares (geometrical structure of MS in a vector space of pseudo-magical squares)
Posted: Jun 18, 1996 8:28 PM

Hi!
I found a base, which helps to create pseudo-magic 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 pseudo-magic Squares create a 3-dimensional-subroom.

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
3-dim-pseudo-magic-square? What have I to do?

I have to find out, if the nxn magic-squares create a geometrical figure
in the vector room, that is built by the pseudo-magical nxn squares? (4x4,
5x5)

Do you have any idea, how to generalize from 3x3 to nxn?

TIA Oliver