Abstract
We call a straight line with one end extending to infinity a light ray. Let h(S n ) be the smallest number such that there exists a finite sphere packing S n + X, with \( X = \left\{ {{\text{o}},{\text{x}}_1 ,{\text{x}}_2 ,...,{\text{x}}_{h\left( {S_n } \right)} } \right\} \) , such that every light ray starting from o is blocked by one of the translates S n + x i , x i ∈ X SHIELA {0}. Similarly, when X is restricted to being a subset of a lattice, we denote the corresponding number by h*(S n ). Hornich proposed the following problem (see L. Fejes Tóth [7]).
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© 1999 Springer-Verlag New York, Inc.
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(1999). Problems of Blocking Light Rays. In: Talbot, J. (eds) Sphere Packings. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22780-1_12
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DOI: https://doi.org/10.1007/978-0-387-22780-1_12
Publisher Name: Springer, New York, NY
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