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research article
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.
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10474_2013_Article_350.pdf
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Publisher's version
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openaccess
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624.46 KB
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