Why is $\pi$ the value it is? Why is the value of  $\pi$ 3.141592...(etc.)? Is it a fundamental property of our universe? Or does it follow from our definition of what a circle is, or does it otherwise follow from the way we perceive or describe the universe?
Could a functioning universe have a  different value of $\pi$? Is it a coincidence that it is a transcendental number and could it just as easily have been rational, or is it a fundamental requirement of pi that it is irrational or transcendental?
Apologies if this has been answered already. I have searched, but all I could find is endless descriptions of how to determine the value of $\pi$, but not why that is the value of $\pi$. Or is "it just is" the only answer we can currently give?
 A: Strange question. This should probably be on MathSE.
There are a million proofs of the irrationality of pi, and why it has to be irrational. You need some reasonable Mathematical knowledge to understand them - it's not like proving the irrationality of root 2. I encourage you to have a look!!
As for the whole "it just is" thing... "It just is" isn't the only answer we can currently give. It's THE answer. Pi is the ratio of the circumference of a circle to it's diameter, among other things. THAT "just is" the case.
Whether it is a fundamental property of our universe is just Philosophy, as far as I'm concerned.
A: It might not be as mysterious as it appears.  Pi is only the consequence of converting from one coordinate system (orthogonal) to another (spherical).  
This exceeds my cleverness, but I think if one created another coordinate system (with some axes 30 degrees apart instead of 90) then there would be some square roots (which are also irrational) in the conversion equations.
So, I am thinking pi is not much weirder than root 2.  Which is still kinda weird.
