I wrote this up in the attached PDF. It's a very short "proof".

I would just like to know if it qualifies as a proof.

All I'm doing is using Archimedes equivalence between a circle and a triangle. And then looking at the hypotenuse of that triangle to see if I can draw any conclusions about the nature of that length. It appears to me that I can safely conclude that the hypotenuse must be an irrational length.

I would just like to know if this is a valid proof and conclusion.

Thank you for your time.

Edited to add: The French mathematician Adrien-Marie Legendre proved in 1794 that pi squared is also irrational. I guess I should cite that in the proof as well huh? Since I have no way of isolating pi in my formula. But since pi squared is also irrational this should still work, right?