scholarly journals Finite Packings of Spheres

1998 ◽  
Vol 19 (2) ◽  
pp. 197-227 ◽  
Author(s):  
U. Betke ◽  
M. Henk
Keyword(s):  
Finite Packings

scholarly journals On Extremal Finite Packings

2002 ◽  
Vol 28 (3) ◽  
pp. 389-403 ◽  
Author(s):  
Schürmann
Keyword(s):  
Finite Packings

Mean projections and finite packings of convex bodies

1994 ◽  
Vol 118 (1-2) ◽  
pp. 41-54 ◽  
Author(s):  
Károly Böröczky
Keyword(s):  
Convex Bodies ◽  
Finite Packings

The Slackness of Finite Packings in E2

1962 ◽  
Vol 69 (6) ◽  
pp. 511-514
Author(s):  
Norman Oler
Keyword(s):  
Finite Packings

Asymptotic Shape of Finite Packings

1998 ◽  
Vol 50 (1) ◽  
pp. 16-28 ◽  
Author(s):  
KáRoly Böröczky ◽  
Uwe Schnell
Keyword(s):  
Convex Body ◽  
Minimal Volume ◽  
Parametric Density ◽  
Asymptotic Shape ◽  
Parallel Body ◽  
Finite Packings

AbstractLet Kbe a convex body in Ed and denote by Cn the set of centroids of n non-overlapping translates of K. Forϱ > 0, assume that the parallel body conv Cn+ϱ K of convCn has minimal volume. The notion of parametric density (see [21]) provides a bridge between finite and infinite packings (see [4] or [14]). It is known that there exists a maximal ϱs(K) ≥ 1/(32d2) such that convCn is a segment for ϱ < ϱs(see [5]). We prove the existence of a minimal ϱc(K) ≤ d+ 1 such that if ϱ > ϱc and n is large then the shape of conv Cn can not be too far from the shape of K. For d= 2, we verify that ϱs= ϱc. For d≥ 3, we present the first example of a convex body with known ϱs and ϱc; namely, we have ϱs= ϱ c= 1 for the parallelotope.

The Slackness of Finite Packings in E 2

1962 ◽  
Vol 69 (6) ◽  
pp. 511 ◽  
Author(s):  
Norman Oler
Keyword(s):  
Finite Packings

On a conjecture of Croft, Falconer and Guy on finite packings

1995 ◽  
Vol 64 (3) ◽  
pp. 269-272 ◽  
Author(s):  
C. Zong
Keyword(s):  
Finite Packings

On the density of finite packings

1985 ◽  
Vol 46 (3-4) ◽  
pp. 205-210 ◽  
Author(s):  
J. M. Wills
Keyword(s):  
Finite Packings

Finite Packings and Parametric Density

2007 ◽  
pp. 332-348 ◽  
Author(s):  
Jörg M. Wills
Keyword(s):  
Parametric Density ◽  
Finite Packings
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