Abstract
In the present note we are going to study the following question proposed by L. Fejes Toth. In the Euclidean plane a lattice Γ is called a holding-lattice of a planar setS if any set congruent toS contains at least one lattice point of Γ. The density of Γ equals (2Δ)−1, where Δ denotes the area of a fundamental triangle of Γ. A holding-lattice ofS of least possible density is said to be the thinnest holding-lattice ofS. The problem: Find the sets whose thinnest holding-lattice is a regular trianglelattice.
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References
Fejes Toth, L.: Personal communication.
Hammer, J.: Unsolved problems concerning lattice points. London-San Francisco-Melbourne: Pitman. 1977.
Santalo, L. A.: Geometria integral de figuras ilimitadas. Publ. Inst. Mato. Rosario, 1, 54.
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To Professor L. Fejes Toth on his 70th Birthday
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Bezdek, K. The thinnest holding-lattice of a set. Monatshefte für Mathematik 103, 177–185 (1987). https://doi.org/10.1007/BF01364338
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DOI: https://doi.org/10.1007/BF01364338