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, ..., "n" – the magic constant is formula_1. For normal magic squares of orders "n" = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence in the OEIS). For example, a normal  8 × 8 square will always equate to 260 for each row, column, or diagonal. The term magic constant or magic sum is similarly applied to other "magic" figures such as magic stars and magic cubes. Number shapes on a triangular grid divided into equal polyiamond areas containing equal sums give polyiamond magic constant. Magic stars. The magic constant of an "n"-pointed normal magic star is formula_2. 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 formula_3. 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.