The irrationality measure of a number x is the largest number μ such that 0 < |x-p/q| < 1/q^μ for infinitely many coprime pairs (p,q), q>0.

It is known that the irrationality measure of any irrational number is at least two, and for almost all numbers, it is exactly equal to 2. π's irrationality measure also has an upper bound on it that is slightly greater than 7 (see the link), and it is known that whether it is ≤ or ≥ 2.5 depends on whether the sequence Σ (csc²n)/n³ converges, though it could be exactly 2.5 regardless of whether the series converges.