4 copies of triangle on sphere can cover entire sphere
Source: Tournament of Towns 2020 oral p5 (15 March 2020)
May 17, 2020
geometry3D geometryspherecombinatorial geometryTilingcoveringcombinatorics
Problem Statement
A triangle is given on a sphere of radius , the sides of which are arcs of three different circles of radius centered in the center of a sphere having less than in length and an area equal to a quarter of the area of the sphere. Prove that four copies of such a triangle can cover the entire sphere.A. Zaslavsky