In observance of Pi Day, I wanted to open up my talk at the graduate algebra seminar to any non-algebra people who might be interested. The talk won't be all algebra, and I think the topic has universal appeal (especially tomorrow). The talk will be one hour and END at 1:59:27 PM.

Abstract:

I will give Ivan Niven's (almost) self-contained proof of the transcendence of pi (mathematically, not existentially) with respect to the usual integers. I will also analyze an unexpected ingredient of the proof which appears in all known proofs of pi's transcendence, and see what happens when we remove it. In particular, I will prove the rationality of pi (mathematically, not psychologically) with respect to the Shepherdson integers.