Geometriae Dedicata

, Volume 117, Issue 1, pp 47–64

On the Number of Tubes Touching a Sphere or a Tube

Article

DOI: 10.1007/s10711-005-9010-7

Cite this article as:
Starostin, E.L. Geom Dedicata (2006) 117: 47. doi:10.1007/s10711-005-9010-7

Abstract

A problem is formulated about how many unit-radius tubes can touch a ball of given radius from the outside and from the inside. Upper bounds for the maximum numbers of contacts are obtained for both interior and exterior contacts. It is also shown that the maximum number of unit-radius tubes touching the same orthogonal cross-section of a particular tube of radius P is [π (arcsin(P+1)−1)−1] and if the number of contacts takes on its maximum, then all tubes are locally aligned.

Keywords

packingtubebialykissing numberspherical codesTammes’ problem

Mathematics Subject Classifications (2000)

52C17

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Max Planck Institute for Physics of Complex SystemsDresdenGermany
  2. 2.Department of Civil and Environmental EngineeringUniversity College LondonLondonU.K