论文标题
小于π/2的厚度的降低球形多边形的几个问题
Several problems on reduced spherical polygons of thickness less than π/2
论文作者
论文摘要
本文旨在解决Lassak关于降低的球形多边形提出的一些问题。主要的结果是表明，常规球形N-辅助的周围在所有固定厚度的固定厚度小于π/2的固定厚度和大多数N顶点中的周长最小。此外，我们确定每个还原的球形多边形的最大直径小于π/2。我们还发现最小的球形半径包含每个还原的球形多边形，其固定厚度小于π/2。
The present paper aims to solve some problems proposed by Lassak about the reduced spherical polygons. The main result is to show that the regular spherical n-gon has the minimal perimeter among all reduced spherical polygons of fixed thickness less than π/2 and with at most n vertices. In addition, we determine the maximal diameter of every reduced spherical polygons with a fixed thickness less than π/2. We also find the smallest spherical radius that contains every reduced spherical polygons with a fixed thickness less than π/2.
