It is commonly believed that the most efficient way to pack a finite number of equal-sized
spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured …

Sphere Packings is one of the most attractive and challenging subjects in mathematics.
Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his …

We show that for any acute ϕ, there exists a covering of S d by spherical balls of radius ϕ
such that no point is covered more than 400 d ln d times. It follows that the density is of order …

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can
explain many of its problems, even the most difficult-such as the sphere-packing problem …

Let J be a system of sets. If all members of J are contained in a given set C and each point of
C belongs to at most one member of J then J is said to be a packing into C. If, on the other …

Given k unit balls in Euclidean d-space Ed, what is the minimal volume of their convex hull?
In E2 hexagonal circle-packings, possibly de-generate, are best possible ([6], In Ed, d Z 5 …

Packings, sausages and catastrophes | Beiträge zur Algebra und Geometrie / Contributions to
Algebra and Geometry Skip to main content SpringerLink Log in Menu Find a journal Publish …

Let B d be the d-dimensional unit ball and, for an integer n, let C n= x 1,..., xn be a packing
set for B d, ie,| xi− xj|≥ 2, 1≤ i< j≤ n. We show that for every p<\sqrt 2 a dimension d (ρ) …

An upper bound for the “sausage catastrophe” of dense sphere packings in 4-space is
given. A basic problem in the theory of finite packing is to determine, for a given positive …

A basic problem of finite packing and covering is to determine, for a given number of k unit
balls in Euclidean d-space E d,(1) the minimal volume of all convex bodies into which the k …