Dissect surface of sphere in eight curvilinear triangles
Source: Germany Bundeswettbewerb Mathematik 2008, Round 2, Problem 3
September 7, 2008
geometry3D geometryspheregeometric transformationreflectioncombinatorics unsolvedcombinatorics
Problem Statement
Through a point in the interior of a sphere we put three pairwise perpendicular planes. Those planes dissect the surface of the sphere in eight curvilinear triangles. Alternately the triangles are coloured black and wide to make the sphere surface look like a checkerboard. Prove that exactly half of the sphere's surface is coloured black.