SEVERAL PROBLEMS ON REDUCED SPHERICAL POLYGONS OF THICKNESS LESS THAN π2
Abstract
We aim 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 π2 and with at most n vertices. In addition, we determine the maximal diameter of every reduced spherical polygons with a fixed thickness less than π2. We also find the smallest spherical radius of a disk that contains every reduced spherical polygons with a fixed thickness less than π2.
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Optimization and Packing Problems
Structural Analysis and Optimization
Publication details
- Journal / source
- Rocky Mountain Journal of Mathematics
- Volume
- 56
- Issue
- 3
- Pages
- 727–739
- Publication date
- 31 July 2026
- Language
- EN