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An extremum problem for the power moment of a convex polygon contained in a disc.
- Source :
-
Advances in Geometry . Oct2021, Vol. 21 Issue 4, p599-609. 11p. - Publication Year :
- 2021
-
Abstract
- In this paper, we investigate an extremum problem for the power moment of a convex polygon contained in a disc. Our result is a generalization of a classical theorem: among all convex n-gons contained in a given disc, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the area functional. It also implies that, among all convex n-gons contained in a given disc and containing the center in those interiors, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the mean of the length of the chords passing through the center of the disc. [ABSTRACT FROM AUTHOR]
- Subjects :
- *JENSEN'S inequality
Subjects
Details
- Language :
- English
- ISSN :
- 1615715X
- Volume :
- 21
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Advances in Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 153013620
- Full Text :
- https://doi.org/10.1515/advgeom-2021-0021