Upper bounds for the perimeter of plane convex bodies

We show that the maximum total perimeter of k plane convex bodies with disjoint interiors lying inside a given convex body C is equal to , in the case when C is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies. As a consequence, we establish a bound on the perimeter of a polygon with at most k reflex angles lying inside a given plane convex body.


Published in:
Acta Mathematica Hungarica, 142, 2, 366-383
Year:
2014
Publisher:
Dordrecht, Springer
ISSN:
0236-5294
Keywords:
Laboratories:




 Record created 2014-04-02, last modified 2018-09-13


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