  It is known that a minimal teaching set of any threshold function on the
twodimensional rectangular grid consists of 3 or 4 points. We derive exact
formulae for the numbers of functions corresponding to these values and further
refine them in the case of a minimal teaching set of size 3. We also prove that
the average cardinality of the minimal teaching sets of threshold functions is
asymptotically 7/2.
  We further present corollaries of these results concerning some special
arrangements of lines in the plane.
