the dirichlet problem (dp) for the laplace operator can be used to model a number of different physical situations. for instance, if the surface of a ball is kept at a given constant temperature f, then the steady state temperature inside the ball is given by the solution of the dirichlet problem in the ball with data f on the sphere. a curious fact is that the solution of the dp with rational data on the unit disk in the plane is rational, whereas the corresponding statement is not true in 3-space (or in any dimension greater than or equal to 3 for that matter). this can be explained by quite elementary methods. refreshments will be served.