Glazyrin, A.Moric, F.2014-04-022014-04-022014-04-02201410.1007/s10474-013-0350-8https://infoscience.epfl.ch/handle/20.500.14299/102342WOS:000331740200007We 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.convex bodydiameterperimeterareageometric inequalitysimple polygonreflex angletext::journal::journal article::research article