Marek Lassak
Packing a planar convex body with three homothetical copies and inscribing relatively equilateral triangles
Let C be a convex body. By C-length of a segment we mean the ratio of the length of this segment to the half of the length of a longest parallel chord of C. We show that every planar convex body C permits an inscribed triangle whose sides are of equal C-length at least 3/2. Equivalently, C can be packed with three equal homothetical copies of ratio at least 3/7 which touch the boundary of C and touch pairwise themselves.
Advances in Geometry, Walter de Gruyter
Print ISSN: 1615-715X
Volume: 5, 04/2005
Pages: 325 - 332
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