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How must n equal circles of given radius be placed so that they cover as great a part of the area of the unit circle as possible? To analyse this mathematical problem, mechanical models are introduced. A generalized tensegrity structure is associated with a maximum area configuration of the n circles, whose equilibrium configuration is determined(More)
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(More)
Amongst the convex polyhedra with n faces circumscribed about the unit sphere, which has the minimum surface area? This is the isoperimetric problem in discrete geometry which is addressed in this study. The solution of this problem represents the closest approximation of the sphere, i.e., the roundest polyhedra. A new numerical optimization method(More)
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