Hello mathgenie99,
Welcome to the LP.
In regards to your question about time pi...Well, I guess with respect to the time-space continuum, constant of time is a "little-more-dominant" than space, as opposed to a space-time continuum where the constant of space is a "little more dominant" than time and "out-of-time" quantum anomalies can occur. We live in both, though the former is more persistent than the latter. This Constant, TIME(4th dimension role), in our 3-dimensional space reality is round - is curved, and infinite. If space is curved, time is curved as well. When you flatten this "circle of time" on a 2-dimensional plane, like on a sheet of paper, it retains that quality of infinity in the form of a number that forever "circles" and has no end in our time-space reality, and This is TIME Pi, which is our old friend 3.14159265.......Was it not Albert Einstein who said, "reality is merely an illusion, albeit a very persistent one." This "persistent reality" is driven by TIME(among other things)...
As for space pi, I don't know. While there is no evidence for it, we can conceptually imagine what it might be it in the meantime, and then we can suppose Space pi would connected to the space-time continuum, which is the "opposite", so to speak, of the time-space continuum as I described above. The Time-space concept and pi works well in an absolute universe where TIME is the constant, and the 3 dimensions of space - length, breadth and height - are uniform. In a space-time continuum, gravity, the velocities of moving objects, along with the perceptions of the observer, can warp time. Time is more shaky in this relative universe, and playing with pi as 3.14159 may be more tricky, which is why pi calculations works best when working with uniformly curved 2-dimensional images on a flat piece of paper. So with usage of space pi for curved objects we can imagine, it would have the ability to transcend a 3-dimensional construct, while accounting for different velocities, perceptions, gravity, and small anomalies that can occur in our reality...Just a crude thought experiment...
Good luck to you...and enjoy the LP!