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Packing and covering a unit equilateral triangle with equilateral triangles. (English) Zbl 1083.52005

The authors deal with packings of equilateral triangles in a unit equilateral triangle \(T\), where the triangles have at least one of its sides parallel to that of \(T\). Let \(t(n)\) be the maximum of the sum of the sides of the triangles in the packing. The authors give upper bounds for \(t(n)\). Analogous problems are considered for the covering case.

MSC:

52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)
52A10 Convex sets in \(2\) dimensions (including convex curves)
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