...but I was looking for a solution more akin to the disk covering problem http://mathworld.wolfram.com/DiskCoveringProblem.html" [Broken] but for a sphere rather than the complex plane extended over a sphere. Maybe if we consider the number of steradian needed to cover a sphere?
As an aside, the Riemann Sphere brings up another question... Is there a 3 dimensional complex space where the traditional complex plane has an orthogonal counterpart sharing the same Real axis?
Since the Surface area of a sphere is 4*pi*r^2 and the area of a disc is pi*r^2 wouldn't you need just 4? This is assuming of course you could manipulate the shape of the discs without changing their area.
Hey Diffy, I came to the same conclusion for the case where the radius of the sphere and the radius of the disks are equal. And when the radius of the sphere is k times the radius of the disks the number is 2k^2. But I can't see how four disks can cover a sphere without being distorted, in which case, the disks are no longer disks...