When you try to put disks in the spaces between disks recursively, you end up after 4 steps with the figure below.
Spherical Geom v01.gh (21.9 KB)
Amazingly, all radius of the successive cirles are natural fractions of one (1, 1/2, 1/3, 1/6, …).
In a podcast at quanta magazine, the mathematican Kontorovich tells some stories about this particular serie of fractions.
