MathDB
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 11, the sides of which are arcs of three different circles of radius 11 centered in the center of a sphere having less than π\pi 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