Several problems on reduced spherical polygons of thickness less than π/2

Cen Liu; Yanxun Chang

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arXiv · 2204.06317

Several problems on reduced spherical polygons of thickness less than π/2

Cen Liu·Yanxun Chang

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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 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.

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Cen Liu, Yanxun Chang. 2022-03-30. Several problems on reduced spherical polygons of thickness less than π/2. https://arxiv.org/abs/2204.06317

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