Firstly, I am aware that this question has been asked twice before. First Time . Second Time.
My question is really about the validitiy of these answers. Note that in the first answer the proof relies on the irrationality of $\pi$, while the second proof only relies on the irrationality of $\sqrt{2}$.
It feels to me that there should be some flaw in this second proof, but I can't say exactly what it is.We see that if she/he were to replace "360" with "$2\pi$" the proof would not work. Any help towards a resolution would be awesome.
A followup question (assuming proof two is wrong): Is there any proof of this that does not rely on the irrationality of $\pi$?