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Pi is a number, a mathematical concept. It doesn't "exist" in a physical sense in the first place (yes, it's the ratio of the circumference of a circle to its diameter, but it also shows up in many surprising equations that are purely numeric and not obviously connected to circles), so it's nonsensical to ask what would happen if it "didn't exist".

If we didn't know about it (which is a very different thing) then ... nothing would happen, other than that we'd have to actually measure the circumference of circles if we wanted to know how big around they were, rather than calculating it from the diameter (which is usually significantly easier to measure).

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Q: What if pi didn't exist?
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