The beginning bit of the physics answer is the answer.
Pi comes from logic, not nature.
This is a bit like when you're trying to ask your kid what the area of the triangle is, and the kid tells you you've drawn the lines bent, or the corners aren't sharp. It's actually not terribly easy to explain to them that they're supposed to understand the idealized entity, and what exactly those ideals are, because you also can't actually draw a triangle with no width and then expect them to appreciate that the qualities you want to expose are somehow exposed when you're breaking your own rules.
Pi comes from logic, not nature.
This is a bit like when you're trying to ask your kid what the area of the triangle is, and the kid tells you you've drawn the lines bent, or the corners aren't sharp. It's actually not terribly easy to explain to them that they're supposed to understand the idealized entity, and what exactly those ideals are, because you also can't actually draw a triangle with no width and then expect them to appreciate that the qualities you want to expose are somehow exposed when you're breaking your own rules.