UPPER BOUND OF DENSITY FOR PACKING OF EQUAL CIRCLES IN SPECIAL DOMAINS IN THE PLANE

Abstract

In the paper we will give heuristic upper bounds for the density of packings of non-overlapping equal circles in a square, an equilateral triangle, and a circle. The area of interstices at the boundary of these domains is calculated with greater precision than by other authors, so the obtained upper bounds are sharper than those known before. Because the function int(x) appears in the relationships, the upper bounds are not monotonous functions of the circle number. Not only the formulae of upper bounds of the maximum packing density are given, but their numerical values are listed up to 30 circles.