2022/04/09 by Christian Bingane, Bingane, Christian, Michael J. Mossinghoff +1
Computer Science · Mathematics · Engineering · #Computational Geometry and Mesh Generation #Mathematics and Applications #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2204.04547
A polygon is small if it has unit diameter. The maximal area of a small polygon with a fixed number of sides n is not known when n is even and n≥14. We determine an improved lower bound for the maximal area of a small n-gon for this case. The improvement affects the 1/n3 term of an asymptotic expansion; prior advances affected less significant terms. This bound cannot be improved by more than O(1/n3). For n=6, 8, 10, and 12, the polygon we construct has maximal area.