Covering Sphere w/ Disks: Min Required Radius k

[Ynaught?]

What is the minimum number of disks required to perfectly cover a sphere with a radius k number of times the radius of the disks?

 

[Werg22]

1/0.

 

[HallsofIvy]

Werg22, he said "sphere", not "ball".

 

[Ynaught?]

Thanks Wergs22 and HallsofIvy,

...but I was looking for a solution more akin to the disk covering problem http://mathworld.wolfram.com/DiskCoveringProblem.html" 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?

 

[Diffy]

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.

 

[Ynaught?]

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...