Abstract
A string of spheres is a sequence of nonoverlapping unit spheres inR 3 whose centers are collinear and such that each sphere is tangent to exactly two other spheres. We prove that if a packing with spheres inR 3 consists of parallel translates of a string of spheres, then the density of the packing is smaller than or equal to\(\pi /\sqrt {18} \). This density is attained in the well-known densest lattice sphere packing. A long-standing conjecture is that this density is maximum among all sphere packings in space, to which our proof can be considered a partial result.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
