Its use is not so linear. By definition, it is most useful, as with the clock, for sectoring.
In the space age, when there are 8 sectors of space to be explored, the sphere contained in said space will be referred to as pi/8. It will serve in coordinate systems also.
Since there is a way to use pi in calculations of both circle area and sphere volume, one might suppose this transcendental number is a bridge to the fourth dimension, right?
So the volume in a four-dimension pi-extended supersphere would be like 9.pi^3, and the spacetime contained something like V.t=9/4.pi^4.