I don't know if this sounds like a crazy man talking, but I think it has to do with the fact that a circle is a regular polygon(I hope the terminology is correct) with an infinite number of sides. This makes the circumference being a never-ending irrational number, and when we divide this number by the diametre we get pi, which also will be an irrational number. Don't trust me completely on this one though, as I'm not sure about it. I think it's right though.