4 May
2018
4 May
'18
3:18 p.m.
Define an open disk on the unit sphere S^2 centered at the point c in S^2 to be a set of the form D = D(c,p,r) = {p in S^2 | dist(p, c) < r} where 0 < r <= pi/2 and dist is distance measured along the sphere. Every such D is contained in some hemisphere. Puzzle: ------- Suppose we have a collection of disjoint open disks on the unit sphere. Is is possible that for every point p of S^2, either p or its antipodal point -p lies inside some disk of the collection? —Dan