It is not, are geometric considerations expressed in the language of maths, it is about the physical universe, all our formulae where Pi appears mean "Pi is a constant 3,14... in Euclidean space"
Does the formula $$\frac{\pi^2}{6} = \sum_{n = 1}^{\infty} \frac 1 {n^2}$$ depend on the local stress-energy tensor?
You could write a paper on how to do real analysis in curved spacetime!
It is not, are geometric considerations expressed in the language of maths, it is about the physical universe, all our formulae where Pi appears mean "Pi is a constant 3,14... in Euclidean space"
But pi and e also come from non-geometrical problems. pi and e are the solutions to the equations
-1 = eix
and
d(xy) / dy = xy