Yup. Sounds easy enough I know; but when I came across the 4-chain [ 1, 17; 2, 2, 16, 16 ] in the output from my search program, I scratched around for a while looking for a bug that (this time) wasn't there, before resorting to computing the inversion, finding the circle coordinates, and plotting the wretched thing. All good exercise to delay the irresistable march of senile decay --- or so I console myself! WFL On 8/21/14, Allan Wechsler <acwacw@gmail.com> wrote:
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
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