56 citations · 56 across the 7 of their papers we have counts for
4 papers · 1 filter
Repeated Patterns of Dense Packings of Equal Disks in a Square
Ronald L. Graham, Boris D. Lubachevsky
We examine sequences of dense packings of n congruent non-overlapping disks inside a square which follow specific patterns as n increases along certain values, n = n(1), n(2),... n…
Curved Hexagonal Packings of Equal Disks in a Circle
B. D. Lubachevsky, R. L. Graham
For each k >= 1 and corresponding hexagonal number h(k) = 3k(k+1)+1, we introduce m(k) = max[(k-1)!/ 2, 1] packings of h(k) equal disks inside a circle which we call "the curved he…
Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio
Boris D. Lubachevsky, Ronald Graham
We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the…
Improving Dense Packings of Equal Disks in a Square
David W. Boll, Jerry Donovan, Ronald L. Graham +1
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packin…