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An extremum problem for the power moment of a convex polygon contained in a disc

An extremum problem for the power moment of a convex polygon contained in a disc AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

An extremum problem for the power moment of a convex polygon contained in a disc

Advances in Geometry , Volume 21 (4): 11 – Oct 26, 2021

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References (15)

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
eISSN
1615-715X
DOI
10.1515/advgeom-2021-0021
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Advances in Geometryde Gruyter

Published: Oct 26, 2021

Keywords: Extremum problem; power moment; convex polygon; dual cross-sectional measure; Jensen’s inequality; 52A40; 52A10; 51M16; 51M20

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