The Finite Pi Paradox: Geometry and the Simulation Logic

Pi is a strictly proven irrational and transcendental constant with an infinite, non-repeating decimal expansion, and calculating it to trillions of digits currently serves primarily as a benchmark for testing supercomputer performance. If Pi were hypothetically found to be finite or repeating, it would cause a collapse of established mathematical and physical systems, forcing a rewrite of geometry and rendering technologies like GPS and integrated circuits theoretically invalid. Furthermore, such a discovery could imply that our universe is not a continuous reality but a discrete, "pixelated" simulation where true randomness and perfect circles are impossible.