A Bent for Magic

Abstract

A semi-magic square of order nisannxn matrix with constant sum along each of its n and n columns. When the two main diagonals also share that same sum with the and columns, the square is called fully magic, A Franklin magic square, on the other hand, is a semi-magic square whose four main rows share the same sum as the and columns, as in the figure below. Each of these three concepts (semi-, fully, and Franklin) has been abbreviated as magic square at various times by different authors, but the meaning is usually clear from context. Finally, a single row, column, diagonal or bent row of a square matrix is called magic if its sum is equal to S = ne, where c is the average of all entries in the matrix and n is the number of rows.