A Simple Proof that π > 3.05

Summary In classrooms where most students are simply told that , accept the fact, and move on, methods for finding lower or upper bound on are usually not taught. Here, I consider a University of Tokyo entrance exam problem: Prove that , I provide students with a simple, yet nontraditional, proof method. In particular, this method does not require a calculator (as in many exams), cumbersome circle geometry, direct use of calculus-based methods, or partial sums of any infinite series.