Again, talking a bit outside my comfort zone, but I believe our universe's physics say that circles only have a fixed circumference-to-radius ratio at "small" (astronomically) scales. At large enough scales space is curved and the ratio begins to change.

In a similar way, a set of different physics would apply to small enough aliens that are principally governed by quantum mechanics. They might never come up with the real numbers because they do not believe that quantities are dense.

We could think of more examples -- aliens who typically move at speeds close to the speed of light would have very different conceptions of time, etc.