On the lengths of curves passing through boundary points of a planar convex shape
Akopyan, Arseniy
Vysotsky, Vladislav
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 &#xbd; 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.
Mathematical Association of America
2017
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/909
Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. 2017;124(7):588-596. doi:<a href="https://doi.org/10.4169/amer.math.monthly.124.7.588">10.4169/amer.math.monthly.124.7.588</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.4169/amer.math.monthly.124.7.588
info:eu-repo/semantics/altIdentifier/issn/00029890
info:eu-repo/semantics/altIdentifier/wos/000413947300002
info:eu-repo/semantics/altIdentifier/arxiv/1605.07997
info:eu-repo/grantAgreement/EC/FP7/291734
info:eu-repo/semantics/openAccess