[Math] Prove that $\pi$ is a transcendental number

Question

Does anyone has a link to a site that confirms that $\pi$ is a transcendental number?

Or, can anyone show how to prove that $\pi$ is a transcendental number?

Thank you in anticipation!

Answer 1

As suggested by Yuval's comment, the most straightforward way of showing that $\pi$ is transcendental proceeds through the Lindemann–Weierstrass theorem that $e^x$ is transcendental if $x$ is (nonzero and) algebraic; since $e^{i\pi}=-1$ is algebraic, then $i\pi$ must be transcendental, and therefore $\pi$ must be (since $i$ isn't rational, but it is algebraic!). You can find a rough proof of the theorem at its Wikipedia page.