A magic square is an n x n array filled with n2 distinct positive integers 1, 2, ..., n2 such that the sum of the n integers in each row, column, and each of the main diagonals are the same. A Latin square is an n x n array consisting of n distinct symbols such that each symbol appears exactly once in each row and column of the square. Many articles dealing with the construction of magic squares introduce the Siam method as a "simple'' construction for magic squares. Rarely, however, does the article actually prove that the construction yields a magic square. In this paper, we describe how to decompose a magic square constructed by the Siam method into two orthogonal Latin squares, which in turn, leads us to a proof that the Siam construction produces a magic square.
"A Proof of the "Magicness" of the Siam Construction of a Magic Square,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 19:
1, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol19/iss1/3