Illuminating and covering convex bodies. (English) Zbl 1303.52009
Summary: Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger’s famous covering problem. Similar numbers can be defined by using proper translates instead of homothets, and even more related concepts make sense. On these lines we introduce some new covering and illumination numbers of convex bodies, present their properties and compare them with each other as well as with already known numbers. Finally, some suggestive examples illustrate that these new illumination numbers are interesting and non-trivial.
MSC:
| 52C15 | Packing and covering in \(2\) dimensions (aspects of discrete geometry) |
Keywords:
parallel illumination; central illumination; illumination numbers; translative coverings; covering numbers; Hadwiger’s covering problemReferences:
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