Abstract.
The paper [3] contains an upper bound to the weighted density of a packing of circles on the unit sphere with radii from a given finite set. This bound is attained by many packings and has applications to problems of solidity. In the present note it is shown that a certain condition imposed on the set of admissible radii can be removed by modifying the original proof of the theorem.
Similar content being viewed by others
References
A Florian (1999) ArticleTitleArchimedean tilings, and solid and non-solid sets of circles Rend Sem Mat Messina Serie II 6 5–12
A Florian (2000) ArticleTitleAn infinite set of solid packings on the sphere Sitzungsber Österr Akad Wiss Math-naturw Kl Abt II 209 67–79 Occurrence Handle1005.52007
A Florian (2001) ArticleTitlePacking of incongruent circles on the sphere Monatsh Math 133 111–129 Occurrence Handle1009.52028 Occurrence Handle10.1007/s006050170026
A Florian (2001–2002) ArticleTitleArchimedean tilings, and solid and non-solid sets of circles II Rend Sem Mat Messina Serie II 8 5–11
A Florian A Heppes (2003) On the non-solidity of some packings and coverings with Circles A Bezdek (Eds) Discrete Geometry Marcel Dekker New York 279–290
J Molnár (1967) ArticleTitleKreispackungen und Kreisüberdeckungen auf Flächen konstanter Krümmung Acta Math Acad Sci Hungar 18 243–251 Occurrence Handle0163.16803 Occurrence Handle10.1007/BF02020979
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Florian, A. Remarks on my paper: packing of incongruent circles on the sphere. Mh Math 152, 39–43 (2007). https://doi.org/10.1007/s00605-007-0481-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-007-0481-5