Why is pi equal to approximately 3.14?

Under what conditions would pi be less, or more than 3.14? What would the universe look like if pi was, say, 1? Is this question even meaningful?

It seems to me that this specific value of pi is a property of the Euclidean space which can be thought of as “flat” (the geometry of the plat piece of paper where angles in a triangle add up to 180 degrees), but that just prompts further questions. Why don’t we revisit the value of pi to account for the curvature of the geometry of our Universe? And is Euclidean geometry special at all? It comes about in a special way, with the introduction of the fifth postulate. But perhaps it’s no more special than some curved geometry and we should look for an explanation in how humans are constructed.

Before these questions can be answered (and some of them may have a decent explanation–here I am exposing my ignorance), I think an important thing to consider is what pi exactly measures and what relationships it plays a role in. For example, suppose that we can imagine a world where pi as given in some measure is equal to 1. Would that mean that every equation in that world that features pi can now safely substitute 1? Probably not — pi may happen to solve a lot of problems; both those that are based on some assumption that we can relax (such as the curvature of the geometry) and others that can’t be tweaked. Presumably, for example, all results that are non-geometric in nature that feature pi will not suddenly magically hold if we change the value of pi (in a way, pi would be no different than e, whose value is purely accidental).