Can this be done in a simplier way? Magic Squares

  • Thread starter Dustinsfl
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  • #1
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Main Question or Discussion Point

Proving Axiom 1 of all 3 x 3 magic squares.

I used summation notation to do so but it is extremely long and cumbersome.

I attached the pdf file with the work.

Is there a way to do this in a simpler more concise manner?
 

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Answers and Replies

  • #2
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I just added the pdf file I forgot to add.
 
  • #3
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What is this axiom 1 that you're trying to prove? That PDF is impenetrable.
 
  • #4
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  • #5
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To form the basis, consider the equations you have regarding some [tex]A[/tex] a magic square, denote [tex]x_i = a_{1i} \in A \quad 1 \le i \le 3[/tex] and [tex]x_i = a_{2i} \in A \quad 4 \le i \le 6[/tex] and so on, then:

[tex]x_1 + x_2 + x_3 = x_4 + x_5 + x_6[/tex]
[tex]x_1 + x_2 + x_3 = x_7 + x_8 + x_9[/tex]
[tex]x_1 + x_4 + x_7 = x_2 + x_5 + x_8[/tex]
[tex]x_1 + x_4 + x_7 = x_3 + x_6 + x_9[/tex]
[tex]x_1 + x_2 + x_3 = x_1 + x_4 + x_7[/tex]

If you play with these equations for a bit you can get the basis matrices.
 

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