B Can physics deal with the existence of Pi?

[A.T.]

It's also very human-centric. Some other species on our planet (and potentially many on other planets) have developed the idea of numbers.

Interesting video on this:

 

[vanhees71]

Perfect points are already pointless ;-).

 

[danielhaish]

with pie being irrational there isn't any problem to describe the world because like the circles you draw the circles in nature are not perfect .
https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/ .
But more amazing fact is that the square root of two is also irrational and so if you take two equally lines put then in angle of 90 degrees , and then connect their edges with a line the line should be exactly the square root of two( Pitagoras sentence)

 

[A.T.]

But more amazing fact is the square root of two is also irrational and so if you take two equally lines put then in angle of 90 and then connect their edges with a line the line should be exactly the square root of two( Protagoras sentence)

It's Pythagoras, and the legend is, that he hated irrational numbers so much, that he had one of his students drowned, for proving they exist:

https://en.wikipedia.org/wiki/Hippasus#Irrational_numbers

 

[Andrew Mason]

with pie being irrational there isn't any problem to describe the world because like the circles you draw the circles in nature are not perfect .

Perhaps e is not an irrational number:

= pie = 2pi
So:
e = 2pi/pi = 2

AM

 

[A.T.]

pie = 2pi

This obvious contraction is one more reason to use tau.

 

[haushofer]

Like this?

Such a waste of pi.

 

[DanielMB]

Why would physics prevent the study of geometry? You can calculate the value of $\pi$ yourself if you know enough calculus to derive the Taylor series for $\tan^{-1}$.

Yes, but if you do that you are using geometric considerations, "Pi" like "e" are derived from geometry and geometry is affected by the stress-energy tensor in GRT, except if you define you are living in a manifold and locally you see "flatland" and in flatland (yes) Pi = 3.14.., and all our formulae where Pi appears are laws from flatland

 

[DanielMB]

Given we live in non-Euclidean spacetime, real Euclidean circles are hard to come by.

$\pi$ is defined purely mathematically; it doesn't rely on the physical universe.

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"

 

[jbriggs444]

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"

A statement that $e^{i\pi}=-1$ is not a statement about the physical universe.

Edit: A mathematician is likely to be supremely dis-interested in the question of what definition of pi is canonical and which definitions are merely provably equivalent.

 

[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.