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.htmCoxeter,
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://www.popmath.org.uk/sculpture/pages/donald.html.