where

is a rational number greater than 1. Also,

is the ratio of

to the radius

. Thus, if

, the sphere resumes its initial configuration every

times around the circle. As an example, if

, a unit sphere rolling around a plane circle of radius

returns to its initial configuration every three times around the circle. The smallest circle with a period of one (i.e., for which the sphere's configuration repeats with each trip around the circle) has the radius

, whereas the smallest circle with a period of two has the radius

.. In general, the smallest circle with period

has radius

.