Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 233-236
Citer cet article
Yu. G. Dutkevich. Diameter of the set of midpoints of chords of a bounded closed set. Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 233-236. http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a11/
@article{MZM_1969_6_2_a11,
author = {Yu. G. Dutkevich},
title = {Diameter of the set of midpoints of chords of a~bounded closed set},
journal = {Matemati\v{c}eskie zametki},
pages = {233--236},
year = {1969},
volume = {6},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a11/}
}
TY - JOUR
AU - Yu. G. Dutkevich
TI - Diameter of the set of midpoints of chords of a bounded closed set
JO - Matematičeskie zametki
PY - 1969
SP - 233
EP - 236
VL - 6
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a11/
LA - ru
ID - MZM_1969_6_2_a11
ER -
%0 Journal Article
%A Yu. G. Dutkevich
%T Diameter of the set of midpoints of chords of a bounded closed set
%J Matematičeskie zametki
%D 1969
%P 233-236
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a11/
%G ru
%F MZM_1969_6_2_a11
The estimate is obtained for the diameter $d(S_n(a))$ of the set $S_n(a)$ of midpoints of chords of length $\ge a$ ($0) of a closed set of diameter 1 in the Euclidean space $E^n$, namely $$ d(S_n(a))\leqslant\begin{cases} 1-a^2/2,&n=2, \\ \sqrt{1-a^2/2},&n\geqslant3, \end{cases} $$ and it is shown that the inequality cannot be improved.
