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)$$

#### About definitions.

##### 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 ) unpublished personal mathematics wiki I am setting up.

## No comments:

## Post a Comment