Was pi invented or discovered?

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So can an imperfect circle have an imperfect, approximate ratio of its circumference divided by its approximate diameter?

We are allowed to describe something as an imperfect circle arent we?

Of course, but you're not making total sense. You need about the first 9 digits (14 digits if you're really anal) of Pi for the area of any "circle" you'll come across in the real world to approximate its area to a meaningful degree of accuracy...

Got it! Thanks.
Approximately somewhere between 9 and 14.

Does that apply for fractions of Pi too?
eg.... Pi ÷ 2 as seen below 1.57