Skip to main content
SpringerLink
Log in

On L. Fejes Tóth’s “sausage-conjecture”

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Letk non-overlapping translates of the unitd-ballB d ⊂E d be given, letC k be the convex hull of their centers, letS k be a segment of length 2(k−1) and letV denote the volume. L. Fejes Tóth's sausage conjecture, says that ford≧5V(S k +B d) ≦V(C k +B d In the paper partial results are given.

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

References

  1. U. Betke, P. Gritzmann and J. M. Wills,Slices of L. Fejes Tóth's sausage conjecture, Mathematika29 (1982), 194–201.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Bonnesen and W. Fenchel,Theorie der konvexen Körper, Springer, Berlin-New York, 1974.

    MATH  Google Scholar 

  3. L. Fejes Tóth,Research problem 13, Period. Math. Hung.6 (1975), 197–199.

    Article  Google Scholar 

  4. H. Hadwiger,Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, 1957.

    MATH  Google Scholar 

  5. P. McMullen,Non-linear angle-sum relations for polyhedral cones and polytopes, Math. Proc. Camb. Phil. Soc.78 (1975), 247–261.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Math. Inst. Univ. Bochum, Universitätsstr. 150, D-4630, Bochum-Querenburg, FRG

    P. Kleinschmidt & U. Pachner

  2. Math. Inst. Univ. Siegen, Hölderlinstr. 3, D-5900, Siegen, FRG

    J. M. Wills

Authors
  1. P. Kleinschmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Pachner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. M. Wills
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleinschmidt, P., Pachner, U. & Wills, J.M. On L. Fejes Tóth’s “sausage-conjecture”. Israel J. Math. 47, 216–226 (1984). https://doi.org/10.1007/BF02760516

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760516

Keywords

Search

Navigation