Evaluation of the Poisson Approximation To Measures of the Random Pattern in the Square

Theoretical values for spacing between points of the Poisson process are frequently used to evaluate the hypothesis that the locations within a region of pointlike objects have a random pattern. These theoretical spacing values are an approximation to spacing values for a uniform process in which the objects are uniformly and independently located in the region. The adequacy of the Poisson approximation to this uniform process for a square region is evaluated by analytic and numeric methods. The approximation is close for a small number of points when spacing between objects is measured by toroidal distance.