Can physics deal with the existence of Pi?

[PeroK]

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!

 

[sophiecentaur]

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 = e^ix
and
d(x^y) / dy = x^y

No geometry explicitly involved there.