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Solution to the lighting problem for zone bodies

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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 anyn-dimensional zone body other than a parallelepiped can be lit by 3·2n−2 pencils of parallel rays or less.

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Authors and Affiliations

  1. Steklov Mathematical Institute, USSR

    V. G. Boltyanskii

Authors
  1. V. G. Boltyanskii
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Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 505–511, November, 1995.

This work was partially supported by the International Science Foundation under grant No. MAT6565-0925.

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Boltyanskii, V.G. Solution to the lighting problem for zone bodies. Math Notes 58, 1029–1032 (1995). https://doi.org/10.1007/BF02305090

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  • DOI: https://doi.org/10.1007/BF02305090

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