Isodiametric Problems for Polygons

The maximal area of a polygon with n = 2m edges and unit diameter is not known when m 5, nor is the maximal perimeter of a convex polygon with n = 2m edges and unit diameter known when m 4. We construct improved polygons in both problems, and show that the values we obtain cannot be improved for large n by more than c1/n3 in the area problem and c2/n5 in the perimeter problem, for certain constants c1 and c2.

• Type: Journal
• Year: 2006
• Where: DCG
• Authors: Michael J. Mossinghoff
• Keywords: DCG 2006, Maximal Area, Maximal Perimeter, Polygons