Coxeter's Loxodromic Sequence of Tangent Circles

An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., R_n, R_n+1, ..., are in geometric progression with ratio


where phi is the golden ratio (Gardner 1979ab). Coxeter (1968) generalized the sequence to spheres.

See also

Arbelos, Bowl of Integers, Golden Ratio, Hexlet, Pappus Chain, Steiner Chain

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Update a linkCoxeter, D. "Coxeter on 'Firmament.' ", H. S. M. "Loxodromic Sequences of Tangent Spheres." Aequationes Math. 1, 112-117, 1968.Gardner, M. "Mathematical Games: The Diverse Pleasures of Circles that Are Tangent to One Another." Sci. Amer. 240, 18-28, Jan. 1979a.Gardner, M. "Mathematical Games: How to be a Psychic, Even if You are a Horse or Some Other Animal." Sci. Amer. 240, 18-25, May 1979b.Robinson, J. "Firmament."

Referenced on Wolfram|Alpha

Coxeter's Loxodromic Sequence of Tangent Circles

Cite this as:

Weisstein, Eric W. "Coxeter's Loxodromic Sequence of Tangent Circles." From MathWorld--A Wolfram Web Resource.

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