The constant $\pi$ is commonly explained in terms of the relationship between the radius and perimeter of a circle, which is a 2-D object. It can also be explained in terms of some infinite series etc. For humans, as we are 3-D beings, the value of $\pi$ is quite critical in our physics. But for an imaginary one-dimensional being, does $\pi$ make any sense other than the sum of some fancy number series?
(In particular, I am curious about physical meanings rather than mathematical.)