Several problems on reduced spherical polygons of thickness less than {\pi}/2
Metric Geometry
2022-04-14 v1 Combinatorics
Abstract
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 {\pi}/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 {\pi}/2. We also find the smallest spherical radius that contains every reduced spherical polygons with a fixed thickness less than {\pi}/2.
Cite
@article{arxiv.2204.06317,
title = {Several problems on reduced spherical polygons of thickness less than {\pi}/2},
author = {Cen Liu and Yanxun Chang},
journal= {arXiv preprint arXiv:2204.06317},
year = {2022}
}