G-2007-56
Simple Polygons of Maximum Perimeter Contained in a Unit Disk
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A polygon is said to be simple if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, for a given integer n, the simple n-sided polygon contained in a disk of radius 1 that has the longest perimeter. When n is even, the optimal solution is arbitrarily close to a line segment of length 2n. When n is odd, the optimal solution is arbitrarily close to an isosceles triangle.
Paru en juillet 2007 , 13 pages
Ce cahier a été révisé en mai 2008
Axe de recherche
Publication
jan. 2009
Simple polygons of maximum perimeter contained in a disk of radius one
, et
Discrete and Computational Geometry, 41(2), 208–215, 2009
référence BibTeX