  General methods for the construction of magic squares of any order have been
searched for centuries. There have been several standard strategies for this
purpose, such as the knight movement, or the construction of bordered magic
squares, which played an important role in the development of general methods.
What we try to do here is to give a general and comprehensive approach to the
construction of magic borders, capable of assuming methods produced in the past
like particular cases. This general approach consists of a transformation of
the problem of constructing magic borders to a simpler - almost trivial - form.
In the first section, we give some definitions and notation. The second section
consists of the exposition and proof of our method for the diferent cases that
appear (theorems 1 and 2). Although methods for the construction of bordered
magic squares have always been presented as individual succesful attempts to
solve the problem, we will see that a common pattern underlies the fundamental
mechanisms that lead to the construction of such squares. This approach
provides techniques for constructing many magic bordered squares of any order,
which is a first step to construct all of them, and finally know how many
bordered squares are for any order. These may be the first elements of a
general theory on bordered magic squares.
