Sure. Take three congruent mutually tangent circles, A, B, and C. Inscribe a smaller circle D so that it is externally tangent to A, B, and C. Inscribe a yet smaller circle E in the triangular void formed by A, B, and D, externally tangent to those three. Then C and E are the "frontiers", and A, B, and D form a three-circle chain between them. On Thu, Aug 21, 2014 at 6:44 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
If I can't stump the list with sequences, I shall try with chains.
The classical (closed) Steiner chain comprises a small frontier circle inside a larger one, with a finite consecutively-touching cyclic sequence of circles occupying the annulus between, each also touching both frontiers.
Is it possible for all circles (including both frontiers) of some (real, non-limiting, non-degenerate) chain to lie external to one another?
WFL
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun