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Tuesday, April 19, 2011

Magic squares of type n-by-n

I wrote a small program that can generate a magic square for any size of a matrix. The idea is that this program can support me in my quest to generate some particular normal magic squares. The ideas I got thus far were too computationally intensive though. It remains an interesting enough playground for me, a challenging enough problem that I might solve one day. - I have read that you need some sort of portfolio of problems on which you can work alternately depending on how you feel, think, etc. on a given moment.

$$\left( \begin{array}{ccc} 9 & 6 & 3 \\ 0 & 6 & 12 \\ 9 & 6 & 3 \end{array} \right)$$
$$\left( \begin{array}{cccc} 9 & 6 & -1 & -4 \\ 5 & -6 & 3 & 8 \\ -8 & 7 & 6 & 5 \\ 4 & 3 & 2 & 1 \end{array} \right)$$
$$\left( \begin{array}{ccccc} 40 & 30 & -46 & 8 & -2 \\ 40 & -43 & 30 & -11 & 14 \\ -52 & 26 & 24 & 22 & 10 \\ -8 & 9 & 16 & 7 & 6 \\ 10 & 8 & 6 & 4 & 2 \end{array} \right)$$
$$\left( \begin{array}{cccccc} 165 & 118 & -86 & -79 & -59 & -38 \\ 84 & -187 & 48 & 46 & 8 & 22 \\ -113 & 42 & 20 & 19 & 36 & 17 \\ -78 & 32 & 15 & 14 & 26 & 12 \\ -43 & 11 & 20 & 18 & 8 & 7 \\ 6 & 5 & 4 & 3 & 2 & 1 \end{array} \right)$$
$$\left( \begin{array}{ccccccc} 344 & 272 & -144 & -180 & -124 & -66 & -46 \\ 228 & -391 & 70 & 68 & 66 & -17 & 32 \\ -202 & 62 & 30 & 58 & 28 & 54 & 26 \\ -194 & 50 & 48 & 46 & 44 & 42 & 20 \\ -94 & 38 & 18 & 34 & 16 & 30 & 14 \\ -40 & 13 & 24 & 22 & 20 & 9 & 8 \\ 14 & 12 & 10 & 8 & 6 & 4 & 2 \end{array} \right)$$
$$\left( \begin{array}{cccccccc} 795 & 644 & -283 & -272 & -261 & -250 & -213 & -124 \\ 493 & -890 & 96 & 94 & 92 & 90 & 17 & 44 \\ -406 & 86 & 42 & 82 & 80 & 39 & 76 & 37 \\ -329 & 72 & 70 & 34 & 33 & 64 & 62 & 30 \\ -252 & 58 & 56 & 27 & 26 & 50 & 48 & 23 \\ -175 & 44 & 21 & 40 & 38 & 18 & 34 & 16 \\ -98 & 15 & 28 & 26 & 24 & 22 & 10 & 9 \\ 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \end{array} \right)$$

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)