An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., , ..., , , , , , , ..., , , ..., are in geometric progression with ratio

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

Coxeter, D. "Coxeter on 'Firmament."' http://www.bangor.ac.uk/SculMath/image/donald.htm

Coxeter, 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." http://atractor.pt/bangor/SculMath-p/image/firm.htm.

CITE THIS AS:

Weisstein, Eric W. "Coxeter's Loxodromic Sequence of Tangent Circles." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CoxetersLoxodromicSequenceofTangentCircles.html