After writing my MathML demo, I wanted to make a quick note of something that I found kinda interesting. First, it uses Euler's Identity (eiπ +1 = 0), written in terms of pi, which results in a fraction of two number which simply don't exist. Then, if you assume that pi can be expressed as a fraction if integers (a/b), it leads to what seems to be a contradiction.
Pi has already been proven to be irrational in many ways, but this one might be the simplest, if it qualifies as a proof at all. The conclusion seems impossible to me, but might not actually be a contradiction.