Skip to main content
SpringerLink
Log in

Polar duals of rotors

  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

AssumeK is a rotor in a regular simplex of heihgt 1 in ann-dimensional Euclidean space. LetK * denote the polar dual ofK. Then the volumeV(K *) satisfies the inequality

$$V(K^* ) \geqslant (n + 1)^n \omega _n ,$$

whereω n denotes the volume of ann-dimensional unit ball. Equality holds if and only ifK is a ball centered at the centroid of the simplex.

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. Chakerian G. D. & Groemer, H., Convex Bodies of Constant Width, Convexity and its Applications (Gruber, P. M., & Wills, J. M., eds.), Birkhäuser, 1983.

  2. Ghandehari, M.,Polar Duals of Convex Bodies, Amer. Math. Soc, to appear. proc.

  3. Goldberg, M.,Rotors in polygons and polyhedra, Math. Comput.,14(1960), 229–239, MR 22, 5934.

    Google Scholar 

  4. Hadwiger, H., Vorlesungen über Inhalt, Oberfläche and Isoperimetrie, Springer-Verlag, Berlin, 1957.

    Google Scholar 

  5. Schneider, R.,Gleitkörper in konvexen polytopen, J. Reine Angew. Math.,248(1971), 193–220, MR 43, 5411.

    Google Scholar 

  6. Yaglom I. M. & Boltyanskii, V. G., Convex Figures, GITTL, Moscow, 1951 (Russian), English transl. by Kelley, P. J. & Walton, L. F., Holt Reinhart and Winston, New York, 1961.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Noval Postgraduate School, 93943, Monterey, CA, USA

    Ghandehari M.

Authors
  1. Ghandehari M.
    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

Ghandehari, M. Polar duals of rotors. Acta Mathematica Sinica 12, 40–42 (1996). https://doi.org/10.1007/BF02109389

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02109389

Keywords

Search

Navigation