Let A, B, and C be spheres that are tangent pairwise and whose points of tangency are distinct. Let {D₁, D₂, ..., 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 = D₁).

What is the value of n?

(In reply to re: mathworld link by Josh70679)

I was referring to the number of circles in the Steiner Chain - the 2-D version.  It can be seen in the animations that the number of (red) circles can be 3, 4, or 5.

Posted by Jer on 2005-11-07 07:39:00