Pansystems methodology and construction of magic squares (Q1581501)

The authors provide several constructions for magic squares. These methods include (i) a recursive method to construct magic squares of order \(n\geq 5\). The construction amounts to recursively building larger and larger borders around a small central square. For example, in order to construct a magic square of order 7, one first starts with a magic square of order 3. One then converts this \(3\times 3 \) square to a magic square of order \(5\). The authors then convert the magic square of order 5 to a magic square of order 7. (ii) Given magic squares of orders \(m\) and \(n\), a method is provided to construct a magic square of order \(mn\). (iii) Given a magic square of order \(m\), a method is provided to construct a magic square of order \(2m\). It is, however, unfortunate that the authors do not provide proofs of their results.