PARTIAL COVERING OF A CIRCLE BY EQUAL CIRCLES. PART II: THE CASE OF 5 CIRCLES

How must n equal circles of given radius r be placed so that they cover as great a part of the area of the unit circle as possible? In this Part II of a two-part paper, a conjectured solution of this problem for n = 5 is given for r varying from the maximum packing radius to the minimum covering radius. Results are obtained by applying a mechanical model described in Part I. A generalized tensegrity structure is associated with a maximum area configuration of the 5 circles, and by using catastrophe theory, it is pointed out that the ''equilibrium paths'' have bifurcations, that is, at certain values of r, the type of the tensegrity structure and so the type of the circle configuration changes.