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October 21

Intersecting spheres

What's the geometric form created by intersecting spheres whose respective radii have an integral ratio, say 3 ? on the line on which their centers reside this is just two points: one inside the segment connecting these centers, and another - out of it. Each intersection create a circle, but all of these circles make a spatial envelope which I'm trying to characterize. Thanks, BentzyCo (talk) 13:45, 21 October 2013 (UTC)[reply]

It'll make a sphere. This is related to the problem of where to fire some flak to try and knock down a plane, there's normally two directions one can aim in if there is any chance at all. Dmcq (talk) 14:48, 21 October 2013 (UTC)[reply]

It sounds like you understand the intersection, but that you're trying to understand the union of the intersection as you vary the positions of the spheres. You'll need to give more detail as to how you're varying them.--80.109.106.49 (talk) 17:08, 21 October 2013 (UTC)[reply]

Hypercube coloring problem

In how many ways can the k-dimensional hypercubes of an n-dimensional hypercube be colored with m colors when two colorings that transform into each other when applying an element of the symmetry group of the n-dimensional hypercube are considered to be identical? Count Iblis (talk) 20:00, 21 October 2013 (UTC)[reply]

See Burnside's lemma#Example application for the k=2, n=3, m=3 case. I doubt there's a closed form expression. --RDBury (talk) 22:15, 21 October 2013 (UTC)[reply]