Path Detection

An industry involved in defense systems can produce a detector that behaves as if it were a circle and knows when an object passes through that circle. The engineer who related this development to us indicated that the cost of production for such a detector is very small so that we can place as many detectors in a field as we wish. However, the detector only knows when, not where, the circumference of its circle is intersected. The question posed was how can we place the sedetectors to be able to locate an object traveling through the field. In this work we present a simplified statement of the physical situation and a model that solves the problem in this simpler setting. We have kept other aspects of the problem, as well as detailed specific ations of the detector, out of this work in deference to the proprietary interests of the industry.