An extremal property of convex hexagons
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 93-96
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The following conjecture is discussed: if $K$ is a plane convex figure and $T$ is a triangle of maximal area contained in $K$, then $K$ is contained in $\sqrt5T$. It is shown that it suffices to check the conjecture in the case where $K$ is a convex hexagon, but the conjecture is proved only in the case where $K$ is a pentagon. Bibl. – 2 titles.
@article{ZNSL_2009_372_a7,
author = {V. V. Makeev},
title = {An extremal property of convex hexagons},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {93--96},
publisher = {mathdoc},
volume = {372},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a7/}
}
V. V. Makeev. An extremal property of convex hexagons. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 93-96. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a7/