Return to Revisions

This critical value is $\alpha_0 \approx 1.3056867$ ... For $\alpha > \alpha_0$ the series converges, for $\alpha < \alpha_0$ it diverges.

Before the inexpensive computer, it was difficult to tell whether the critical value is ${}> 1$ or not.

Boyd, David W. The sequence of radii of the Apollonian packing. Math. Comp. 39 (1982), no. 159, 249–254.

http://www.ams.org/mathscinet-getitem?mr=658230