  We aim to connect the non commutative geometry ``quotient space'' viewpoint
with the standard super Yang Mills theory approach in the spirit of
Connes-Douglas-Schwartz and Douglas-Hull description of application of
noncommutative geometry to matrix theory. This will result in a relation
between the parameters of a rational foliation of the torus and the dimension
of the group U(N). Namely, we will be provided with a prescription which allows
to study a noncommutative geometry with rational parameter p/N by means of a
U(N) gauge theory on a torus of size \Sigma / N with the boundary conditions
given by a system with p units of magnetic flux. The transition to irrational
parameter can be obtained by letting N and p tend to infinity with fixed ratio.
The precise meaning of the limiting process will presumably allow better
clarification.
