For a real number x, the irrationality index μ(x) is a way of measuring how well x can be approximated by rational numbers. If x is rational, μ(x) = 1. If x is irrational, μ(x) ≥ 2. OpenAI recently published a proof that μ(π) = 2. Almost all real numbers have irrationality exponent 2, so the new result says […] The post Irrationality exponent of π first appeared on John D. Cook.