Symmetrical close packing of cylindrical objects

Optimal regular close packing of cylindrical objects has many applications in diverse fields of study. Close-packed cylindrical objects are placed tangent to one another in such a way as to minimize the area of the circumscribing circle. Beginning with an initial ring of P objects additional cylinders are added in concentric rings of A * P cylinders outside prior rings. The study of close packing will provide effective methods for geometric placement for self-organizing systems in order to minimize the area used for a given number of units, as well as the logistical task of populating a circuit board with a large number of cylindrical components. The focus of this research is to establish a framework for analyzing concentric close packing geometry for large systems. An algorithm for computing the arrangement of large systems has been developed and initial inquiries into the behavior of the A multiplier at each step have been made.