I think touching π would take a lot more effort than simply touching a ruler. First of all, we cannot prove the consistency of our hands’ motion. Secondly, say if our motions are consistent, it might be impossible to touch every atom on the ruler. Looking in an atomic view, the ruler does not have a flat surface, and due to its production process, it’s material might have different densities, which makes it almost impossible to touch π.
Besides, how can we confirm that things like πexist in the first place? There’s no physical representation for theories and names. We can conveniently describe our world using theories and establish it as facts and truths, but who knows, maybe none of that exists.