Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 234-238
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V. V. Makeev. A kinematic formula for affine diameters and affine medians of a convex set. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 234-238. http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a16/
@article{ZNSL_2001_280_a16,
author = {V. V. Makeev},
title = {A kinematic formula for affine diameters and affine medians of a convex set},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {234--238},
year = {2001},
volume = {280},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a16/}
}
TY - JOUR
AU - V. V. Makeev
TI - A kinematic formula for affine diameters and affine medians of a convex set
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 234
EP - 238
VL - 280
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a16/
LA - ru
ID - ZNSL_2001_280_a16
ER -
%0 Journal Article
%A V. V. Makeev
%T A kinematic formula for affine diameters and affine medians of a convex set
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 234-238
%V 280
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a16/
%G ru
%F ZNSL_2001_280_a16
For a planar convex set $K$ with $C^2$-smooth boundary, the area of the set of the points lying on a given number of affine diameters of $K$ is estimated. As a corollary, it is proved that the area of $K$ is at most $\pi M^2/4$, where $M$ is the largest length of a chord of $K$ halving the area of $K$.
