---
res:
bibo_abstract:
- We study the lengths of curves passing through a fixed number of points on the
boundary of a convex shape in the plane. We show that, for any convex shape K,
there exist four points on the boundary of K such that the length of any curve
passing through these points is at least half of the perimeter of K. It is also
shown that the same statement does not remain valid with the additional constraint
that the points are extreme points of K. Moreover, the factor ½ cannot
be achieved with any fixed number of extreme points. We conclude the paper with
a few other inequalities related to the perimeter of a convex shape.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Arseniy
foaf_name: Akopyan, Arseniy
foaf_surname: Akopyan
foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-2548-617X
- foaf_Person:
foaf_givenName: Vladislav
foaf_name: Vysotsky, Vladislav
foaf_surname: Vysotsky
bibo_doi: 10.4169/amer.math.monthly.124.7.588
bibo_issue: '7'
bibo_volume: 124
dct_date: 2017^xs_gYear
dct_identifier:
- UT:000413947300002
dct_isPartOf:
- http://id.crossref.org/issn/00029890
dct_language: eng
dct_publisher: Mathematical Association of America@
dct_title: On the lengths of curves passing through boundary points of a planar
convex shape@
...