B Can physics deal with the existence of Pi?

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The discussion centers on the existence of Pi and its relationship with physics and mathematics. Participants clarify that Pi is a mathematical constant defined as the ratio of a circle's circumference to its diameter, independent of physical reality. They argue that numbers, including Pi, exist conceptually within human understanding rather than in the physical world. The conversation also touches on the implications of defining existence in mathematical terms versus physical terms, emphasizing that Pi's existence is not contingent on the physical universe. Ultimately, the consensus is that Pi exists as a mathematical truth, regardless of whether it can be physically realized.
  • #61
DanielMB said:
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!
 
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  • #62
DanielMB said:
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

No geometry explicitly involved there.
 

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