The irrationality exponent of π is 2
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalization proves that the irrationality exponent of $\pi$ is exactly two. For every $\nu>2$, all sufficiently large positive denominators $q$ satisfy $|\pi-p/q|\ge q^{-\nu}$ for every integer numerator $p$. It also states the exact supremum characterization using infinitely many rational approximations.
The paper's convergence consequence for the Flint–Hills series is outside this selected statement.
Comparator links
| Result | Comparator statement |
|---|---|
| The irrationality exponent of $\pi$ equals two | PiExponent.lean |