Let A, B, and C be spheres that are tangent pairwise and whose points of tangency are distinct. Let {D_{1}, D_{2}, ..., D_{n}} be a set of spheres each of which is tangent to spheres A, B, and C. For i = 1 to n, D_{i} is externally tangent to D_{i+1} (where D_{n+1} = D_{1}).
What is the value of n?
If two of the spheres A,B,C are internal to the third the situation is as:
http://mathworld.wolfram.com/Hexlet.html
And the solution is n=6
If A,B,C are are externally tangent, I think the solution can also be 6 counting a sphere at infinity
Related is the Steiner Chain:
http://mathworld.wolfram.com/SteinerChain.html
but the number of circles is not limited.

Posted by Jer
on 20051104 12:47:40 