---
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/0002-9890
  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@
...