Okay, yes, Pi is a mathematical constant; I think the issue here is the
applicability of Pi, in relating numbers and math to our observations
of the physical universe.
In many ways, it's a remarkable coincidence that Pi is useful at all - it implies that our physical universe is Euclidean in nature, with three
dimensions, perpendicular to each other.
But that's not really correct, apparently, from
other observations we have made about the physical universe. It turns out that space-time can
warp, and the dimensions of width, height, and depth, are
not always perpendicular to each other.
When that's the case, a circle existing in that space does
not have a circumference to diameter ratio equal to Pi. It's slightly
different.
Imagine a circle that's drawn on the surface of a sphere. The diameter you measure of that circle, on the surface of the sphere, is a curved arc -
and the ratio you get is
not Pi. That curved arc, from the point of view of someone on the surface of the sphere, looks like a 'straight
line'.
That's similar to how our space-time, in 3d, can be warped into a 4th dimension, just like a 2d surface can be warped onto the 3rd dimension of a
sphere.
The amazing thing is that we, as humans, exist on such a scale, and in such a narrow band of consistent physical properties, that the universe seem to
act 99.999% Euclidean. We need to get close to black holes, accelerate to a significant fraction of light-speed, or other extreme changes in order
for the warped nature of space-time to be apparent.
3.14, or 22/7, is a good enough approximation for day-to-day use.