论文标题
小面积的小多边形
Small polygons with large area
论文作者
论文摘要
如果多边形为单位直径，则是\ textit {small}。当$ n $均匀且$ n \ geq14 $时，尚不清楚带有固定数量$ n $的小多边形的最大面积。我们确定了针对这种情况的小$ n $ gon的最大面积的改进的下限。改进会影响渐近扩展的$ 1/n^3 $条款；事先进步影响了较少的重要条款。该界限不能提高超过$ O（1/n^3）$。对于$ n = 6 $，$ 8 $，$ 10 $和$ 12 $，我们构造的多边形具有最大面积。
A polygon is \textit{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 $n\geq14$. We determine an improved lower bound for the maximal area of a small $n$-gon for this case. The improvement affects the $1/n^3$ term of an asymptotic expansion; prior advances affected less significant terms. This bound cannot be improved by more than $O(1/n^3)$. For $n=6$, $8$, $10$, and $12$, the polygon we construct has maximal area.
