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Mat. Zametki, 1995, Volume 58, Issue 4, Pages 505–511 (Mi mz2071)  

This article is cited in 4 scientific papers (total in 4 papers)

Solution to the lighting problem for zone bodies

V. G. Boltyanskii

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In the paper, the class of zone bodies, which includes, in particular, zonoids (and zonohedrons) is introduced. The lighting problem for this class is solved, thus generalizing earlier results for zonohedrons (H. Martini) and zonoids (V. G. Boltyanskii and P. S. Soltan). Namely, it is proved that the boundary of any $n$-dimensional zone body other than a parallelepiped can be lit by $3\cdot2^{n-2}$ pencils of parallel rays or less.

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English version:
Mathematical Notes, 1995, 58:4, 1029–1032

Bibliographic databases:

Received: 28.02.1994

Citation: V. G. Boltyanskii, “Solution to the lighting problem for zone bodies”, Mat. Zametki, 58:4 (1995), 505–511; Math. Notes, 58:4 (1995), 1029–1032

Citation in format AMSBIB
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\by V.~G.~Boltyanskii
\paper Solution to the lighting problem for zone bodies
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 4
\pages 505--511
\mathnet{http://mi.mathnet.ru/mz2071}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1378331}
\zmath{https://zbmath.org/?q=an:0856.52014}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 4
\pages 1029--1032
\crossref{https://doi.org/10.1007/BF02305090}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TW84800023}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Boltyanskii, “Hindering systems for convex bodies”, Sb. Math., 188:3 (1997), 327–339  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Boltyanski, VG, “Solution of the illumination problem for three-dimensional convex bodies”, Doklady Mathematics, 62:3 (2000), 353  mathnet  mathscinet  zmath  isi
    3. Boltyanski, V, “Solution of the illumination problem for bodies with md M=2”, Discrete & Computational Geometry, 26:4 (2001), 527  mathscinet  zmath  isi
    4. Bezdek K., Khan M.A., “The Geometry of Homothetic Covering and Illumination”, Discrete Geometry and Symmetry: Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60Th Birthdays, Springer Proceedings in Mathematics & Statistics, 234, eds. Conder M., Deza A., Weiss A., Springer, 2018, 1–30  crossref  mathscinet  isi  scopus
  • Математические заметки Mathematical Notes
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