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Packing a planar convex body with three homothetical copies and inscribing relatively equilateral triangles
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Marek Lassak
Published/Copyright:
July 27, 2005
Abstract
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.
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Published Online: 2005-07-27
Published in Print: 2005-04-20
© de Gruyter
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- Packing a planar convex body with three homothetical copies and inscribing relatively equilateral triangles
Articles in the same Issue
- Localization of automorphisms of some unbounded Levi degenerate algebraic hypersurfaces in ℂn
- Virtual and non-virtual algebraic Betti numbers
- The classification of flag-transitive Steiner 3-designs
- On surfaces with two apparent double points
- Halphen conditions and postulation of nodes
- Topological affine planes with affine connections
- The embedding of (0, 2)-geometries and semipartial geometries in AG(n, q)
- The geometry of isoparametric hypersurfaces with four distinct principal curvatures in spheres
- New counterexamples to A. D. Alexandrov’s hypothesis
- A maximum principle for parabolic equations on manifolds with cone singularities
- Packing a planar convex body with three homothetical copies and inscribing relatively equilateral triangles
