Details of Ivan Niven Proof of the Irrationality of Pi

To prove that pi is irrational, you have to show that the assumption that it is rational leads to a contradiction of some sort. How one goes about doing this gives rise to the many different proofs that pi is irrational.  One such argument is presented by Ivan Niven in the Bulletin of the American Mathematical Society in 1947. That argument fits easily on a single page.....presenting itself more like a note.

The note definitely contains the keys to his argument but as mathematicians often do, he leaves the details to the reader. In the paper Details of Ivan Niven Proof that pi is Irrational those details along with some background refreshers are supplied by this author.