A 10x10 square can obviously hold 100 unit circles (diameter=1) when arranged in rows and columns. What is the maximum number of non-overlapping unit circles a 10x10 square can hold if the circles are packed closer together?

Arranging of the unit circles in two sets of honeycomb lattices of five rows each -- with the outer two and middle row of each set having ten circles surrounding rows of nine-- will have an area used of approximately 10x[8.928203] square units for the 96 circles. This remaining area is large enough to place another row of ten unit circles for a total count of 106.

Posted by Dej Mar on 2008-05-30 08:38:03