Skip to main content
SpringerLink
Log in

Covering convex solids by greater homotheties

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Let K be a convex solid of Euclidean space En, with bd K and int K being its boundary and interior. The paper solves the problem of the possibility of covering K by sets homothetic to int K, with the ratio of the homotheties being greater than unity and the centers being in En/int K, while, should such a covering exist, an estimate is provided of the least cardinality of the family of sets covering K.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. H. Hadwiger, “Ungelöste Probleme,” No. 20, Elem. der Math.,12, 121 (1957).

  2. I. Ts. Gokhberg and A. S. Markus, “A problem of covering convex figures by similar ones,” Izv. Mold. Fil. Akad. Nauk SSSR, No. 10 (88)), 87–90 (1960).

    Google Scholar 

  3. V. G. Boltyanskii, “Problem of illuminating boundaries of a convex solid,” Izv. Mold. Fil. Akad. Nauk SSSR, No. 10 (76), 77–84 (1960).

    Google Scholar 

  4. P. S. Soltan, “On the illumination from within of the boundary of a convex solid,” Matem. Sb. (Nov. Seriya),57 (99), 443–448 (1962).

    Google Scholar 

  5. V. G. Boltyanskii and I. Ts. Gokhberg, Theorems and Problems of Combinatory Geometry [in Russian], Moscow (1965).

  6. P. S. Soltan, “Illumination from within for unlimited convex solids,” Dokl. Akad. Nauk SSSR,194, No. 2, 273–274 (1970).

    Google Scholar 

  7. B. Grünbaum, “Fixing systems and inner illumination,” Acta Math. Acad. Sci. Hung.,15, 161–163 (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kishinev State University, USSR

    P. S. Soltan

Authors
  1. P. S. Soltan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 85–90, July, 1972.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Soltan, P.S. Covering convex solids by greater homotheties. Mathematical Notes of the Academy of Sciences of the USSR 12, 483–485 (1972). https://doi.org/10.1007/BF01094396

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01094396

Keywords

Search

Navigation