Abstract
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, a 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.
Article PDF
Similar content being viewed by others
References
Brass, P., Moser, W., Pach, J.: Research Problems in Discrete Geometry. Springer, New York (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
Work of the first author was supported by NSERC grant 239436-05, AFOSR FA9550-07-1-0302, and ExxonMobil. Work of the second author was supported by NSERC grant 105574-02.
Rights and permissions
About this article
Cite this article
Audet, C., Hansen, P. & Messine, F. Simple Polygons of Maximum Perimeter Contained in a Unit Disk. Discrete Comput Geom 41, 208–215 (2009). https://doi.org/10.1007/s00454-008-9093-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00454-008-9093-7