The area of reduced spherical polygons

Abstract

We confirm two conjectures of Lassak on the area of reduced spherical polygons. The area of every reduced spherical nonregular $n$-gon is less than that of the regular spherical $n$-gon of the same thickness. Moreover, the area of every reduced spherical polygon is less than that of the regular spherical odd-gons of the same thickness and whose number of vertices tends to infinity.