4 papers
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…
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…
Generalized de Bruijn Cycles
Joshua N. Cooper, Ronald L. Graham
For a set of integers , we define a -ary -cycle to be a assignment of the symbols 1 through to the integers modulo so that every word appears on some translate o…