Pi is only incidentally a number. Pi is an abstraction that represents a certain relationship. (Actually more of a set of relationships.) If you define pi as a

Pi is only incidentally a number. Pi is an abstraction that represents a certain relationship. (Actually more of a set of relationships.) If you define pi as a specific constant with limited precision - because "that's all physical systems need" - you lose insights into the web of relationships around it. This is a bad thing and makes many kinds of math harder. It's the conceptual equivalent of lossy data compression. You don't want to do it unless you really, really need to. And if you do it, you need to be aware that you're now using approximations instead of abstractions, and those are not the same thing.