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Magic constant

The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order n – that is, a magic square which contains the numbers 1, 2, ..., n2 – the magic constant is .

Magic stars
The magic constant of an n-pointed normal magic star is M = 4n + 2. ==Magic series==
Magic series
In 2013 Dirk Kinnaes found the magic series polytope. The number of unique sequences that form the magic constant is now known up to n=1000. ==Moment of inertia==
Moment of inertia
In the mass model, the value in each cell specifies the mass for that cell. This model has two notable properties. First it demonstrates the balanced nature of all magic squares. If such a model is suspended from the central cell the structure balances. (consider the magic sums of the rows/columns .. equal mass at an equal distance balance). The second property that can be calculated is the moment of inertia. Summing the individual moments of inertia (distance squared from the center × the cell value) gives the moment of inertia for the magic square, which depends solely on the order of the square. ==See also==
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