Pi is just tue circle ratio, we can calculate it to a far higher degree than we can ever physically measure it. On some scales space no longer appears discrete so circles... well any physical circle will be an approximation in the first place, if we imagine a circle running in space (and we approximate that space as flat) eventually we will be measuring it below the plank lenght where distances are no longer meaningful (due to quantum mechanics)
Circles are thus mathematical constructs which don't exist in reality. Pi is just the circle ratio which is an idea we can express, and fundamental to the idea of flat 2
space (ie Euclidean Geometry) is that circles have a ratio of cirumfrence to diameter of a number i shall define as Tau/2
It's an idea, and we can comprehend the idea of Pi being infinite and non-repeating without necessarily knowing more the three digits of Pi.
The idea of space expanding forever is a though one. It kinda depends a lot one the global geometry of the Universe, is the Universe simply connected? Could you continue travelling through space and eventually return to your original position? (like on the surface of an expanding balloon?) if we imagine the Universe is like an expanding surface embedded in a 3
space but infact a 3
space embedded in a 4
superspace, then that implies the existance of another spatical dimension and some constraint holding us in this space... But we can also imagine it to be a 3
curved space not embedded in anything, and the black hole cause so much curvature they essentially create one-way loops, inside the loop there is no way back...
We have theories of Multi-dimensional (meme)Branes, which would have universes sitting on them and as they spread apart they would drag the expansion of that universe, or as they collided with each other thet would cause a big bang type event. But these theories have no testable basis, thus we can gather no evidence for or against them (at present)
In a more classic sense, we would imagine the 3
space we live in expanding not into anything. Just streching itself. Space is just a measure, it doesn't need to expand into anyfhing, and expanding forever will always still remain finite in a finite amount of time (if space is finite to being with, and again we don't know anything about the Universe's global geometry, it could be toroidal, it could be infinite, it could be saddle shaped..)