  The normal or Gaussian distribution plays a prominent role in almost all
fields of science. However, it is well known that the Gauss (or Euler--Poisson)
integral over a finite boundary, as it is necessary for instance for the error
function or the cumulative distribution of the normal distribution, cannot be
expressed by analytic functions. This is proven by the Risch algorithm. Still,
there are proposals for approximate solutions. In this paper, we give a new
solution in terms of normal distributions by applying a geometric procedure
iteratively to the problem.
