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Disks and sphere

  1. Mar 18, 2008 #1
    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?
    Last edited: Mar 18, 2008
  2. jcsd
  3. Mar 19, 2008 #2
  4. Mar 20, 2008 #3


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    Werg22, he said "sphere", not "ball".
  5. Mar 28, 2008 #4
    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?
  6. Mar 28, 2008 #5
    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.
  7. Mar 28, 2008 #6
    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...
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