Was pi invented or discovered?

[The Grand Nudger]

Fair enough, but the reason that they aren't perfect representations of said concept is that we have devised said concepts requirements in a way that excluded them. We could just as easily have defined a circle as a concept referring to the exact dimensions of the sun or ripples on a pond (or some equivalent ratio thereof). Had we done so, pi (not our pi, but thi sun pi we've never gone to the truoble of defining) would still exist, there would still be a relationship between the various dimensions ad ways of measuring the sun that yielded a guide as to what a circle was - and it would reside in the real world as filled with substance and material as the dimensions of any circle in our minds - based upon those relationships which exist in the real world and are contingent upon those properties of that world that we can detect - exemplified by the sun, as our prime example.

Our concept of a circle (and our determinations of what is or is not a cricle) have changed over time...but it's more than fair to describe our initial concept of a circle as something very similar to what a child today might point to when asked to show an example of a circle. The group of things the child singles out will not be circles as we now understand them, nor will the child leverage or likely understand pi, but they will still be circles, and the concept is still very useful in describing those things.

It shouldn't be surprising that a system refined for the systems sake begins to become divorced from what it was initially crafted to communicate. All that is required to show where a circle (or pi) resides in the world outside that system is for dimensions to exist, for an area to be singled out and the relationship between the borders of that area quantified in any way, if we single out a circular area, this will plainly demonstrate where pi resides and where it waited to be discovered in hard inches (if you will). Regardless of what we call that area (if not a circle) and regardless of the manner in which it is quantifed (if not the numbers and math you and I are familiar with). Whatever concept devised and whatever system leveraged to study this area will yield a result that is equivalent to our own. IOW, a rose by any other name.