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## Tuesday, April 19, 2011

### Magic squares of type 5-by-5

Still in 're-discovery mode' generating magic squares has become trivial, although the computational resources increase fast depending on the size of the square.
$$\left( \begin{array}{ccccc} 14 & 32 & 6 & 8 & 22 \\ 14 & 7 & 30 & 17 & 14 \\ 0 & 26 & 24 & 22 & 10 \\ 44 & 9 & 16 & 7 & 6 \\ 10 & 8 & 6 & 28 & 30 \end{array} \right)$$
$$\left( \begin{array}{ccccc} 4 & 22 & 6 & 28 & 42 \\ 4 & 37 & 30 & 17 & 14 \\ 20 & 26 & 24 & 22 & 10 \\ 64 & 9 & 16 & 7 & 6 \\ 10 & 8 & 26 & 28 & 30 \end{array} \right)$$
$$\left( \begin{array}{ccccc} 4 & 6 & 22 & 26 & 64 \\ 6 & 55 & 30 & 17 & 14 \\ 16 & 34 & 24 & 42 & 6 \\ 86 & 7 & 16 & 7 & 6 \\ 10 & 20 & 30 & 30 & 32 \end{array} \right)$$

##### Magic square
A magic square is a square matrix with elements in $\mathbf{Z}$ such that the totals of rows, columns and both diagonals are equal.
##### Normal magic square
A normal magic square is a magic square with elements $1,2, \cdots, n^2$ where $n$ is the size of the matrix.
##### Latin square
A latin square is a $n$ by $n$ square matrix containing $n$ times the first $n$ elements of the alphabet such that each row and each column contains each letter only once. (i.e. Cayley Table)

#### Further developments

Clearly, normal magic squares are the most desirable objects in the realm of matrices. I am making detailed notes about this work in the ( still? ) unpublished personal mathematics wiki I am setting up.

## 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.)