Further characterization of ellipsoids
In this paper the following result is proved: Let K be a planar convex body and let γ be a differentiable closed convex curve. If for every point p in the interior of K the set of the midpoints, of all the chords through p , are forming a curve α ( p ) which is directly homothetic to γ , then K is a...
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| Veröffentlicht in: | Monatshefte für Mathematik 2010-04, Vol.160 (1), p.73-80 |
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| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper the following result is proved: Let
K
be a planar convex body and let
γ
be a differentiable closed convex curve. If for every point
p
in the interior of
K
the set of the midpoints, of all the chords through
p
, are forming a curve
α
(
p
) which is directly homothetic to
γ
, then
K
is an ellipse. |
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| ISSN: | 0026-9255 1436-5081 |
| DOI: | 10.1007/s00605-008-0091-x |