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Homemagic square

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# magic square

A magic square of order $n$ is an $n\times n$ array using each one of the numbers $1,2,3,\ldots,n^{2}$ once and such that the sum of the numbers in each row, column or main diagonal is the same.

Example:

$\begin{pmatrix}8&1&6\\ 3&5&7\\ 4&9&2\end{pmatrix}$ |

It’s easy to prove that the sum is always $\frac{1}{2}n(n^{2}+1)$. So in the example with $n=3$ the sum is always $\frac{1}{2}(3\times 10)=15$.

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more general by alozano ✓

## Comments

## Separate article for magic constant or put in here?

Both Mathworld and Wikipedia have separate articles for magic constant. Should PlanetMath also have a separate magic constant entry (as a child object of magic square) or should this be added to this entry, perhaps as a section?

## Re: Separate article for magic constant or put in here?

My vote would be for magic constant having an entry of its own. My thinking behind this is that a person who would want to read about either a magic constant or a magic square can do so without having to make their way through other material that they might not care about. In short, it would enable others to access the information they want more quickly. That's my two cents.

## Re: Separate article for magic constant or put in here?

Good point! My two cents is that then I don't have to worry about link-escaping "constant" if I write "magic constant."