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http://arxiv.org/pdf/1504.0054...
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arXiv.org e-Print Archive
Preprint . 2015
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Article . 2015
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Reflections of Planar Convex Bodies

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint , Other literature type 01 Jan 2016Embargo end date: 01 Jan 2015Publisher:Springer International Publishing
Authors: Schneider, Rolf;

doi: 10.1007/978-3-319-28186-5_6 , 10.48550/arxiv.1504.00541

arXiv: 1504.00541

Reflections of Planar Convex Bodies

Abstract

It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent points with this property.

7 pages

Related Organizations
Keywords

Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), 52A10 (Primary)

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 6
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Average
Green