Nomograph for the Determination of the Common Area of Intersection of Two Distributed Circles

摘要

When two circles are distributed with a specified probable error about a common center, the question naturally arises as to the area of intersection or overlap. This is not a constant but will follow a probability distribution determined by the distances between centers. It was the purpose of this report to develop a nomograph to determine the expected least upper bound of the area overlap at any prescribed level of assurance. The problem consists of two parts. One of these is to determine the area of intersection of two arbitrary circles as a function of the separation of their centers. The second problem is to find the statistical distribution of the distances between centers. In the third section, this is shown to be the same distribution of a point of impact from its intended center of impact, providing the centers have a common circular gaussian normal distribution.