 A simple proof that pi is irrational by Ivan Niven

Bulletin of the American Mathematical Society 53(6), page 509. DOI: doi.org/10.1090/S0002-9904-1947-08821-2

One-page original article scan: nonagon.org/ExLibris/sites/default/files/pdf/Niven-Pi-Irrational.pdf

The factorial-normalized polynomial, its integer endpoint derivatives and the positive integral tending to zero provide the complete elementary proof.