there is no isometry mapping this spherical bowl to a subset of the plane.
Source: Polish MO Second Round 1976 p3
September 8, 2024
geometry3D geometryspherecombinatorial geometry
Problem Statement
We consider a spherical bowl without any great circle. The distance between points and on such a bowl is defined as the length of the arc of the great circle of the sphere with ends at points and , which is contained in the bowl. Prove that there is no isometry mapping this bowl to a subset of the plane.Attention. A spherical bowl is each of the two parts into which the surface of the sphere is divided by a plane intersecting the sphere.