I was just reading through some random articles on the proofs (or lackthere of) of some famous constants being irrational or transcendental. (Such as $ \pi, e$, the Euler-Mascheroni constant etc.)
Obviously $\pi$ and $e$ are known to be transcendental but the Euler-Mascheroni hasn't even been proven to be irrational although most suspect it is transcendental from what I've read.
So what I'm wondering about is if anyone is familiar with examples of any constants in science that were thought to irrational/transcendental but were later proven to be rational.
I'm already aware of Legendres Constant (that is the constant in the asympyotic expression of the prime counting function) was proven to be exactly $1$. So I'm curious if there are other examples of a similar situation to Legendre.
When Onsager found the critical exponents for the 2D Ising model, they turned out to be rational numbers.