Was pi invented or discovered?

[Anomalocaris]

This one should be easy to answer. It was invented, like most (if not all) of mathematics. Various reasons:

1) Pi is a number; numbers don't "exist" in the physical world; they only exist in mathematics, which is an invention of humanity. Now, granted physics is also an invention of humanity, but physics at least is looking at the physical world and describing it. There is nothing in the physical world you can look at and say "that's a number 1" (though obviously you can use numbers when interpreting the real world..."there are 3 cows in the field", etc.)

2) Not only is Pi a number, it's an irrational number, which means it's infinitely long (among other things). You don't get infinities in the real world (as far as we know), so there is no way for Pi to exist in the real world. Even we can't calculate the true value of Pi, since we don't have enough material / energy in the universe to do it.

3) Slightly related to point 2. Pi is generated by taking the circumference of a circle and dividing it by it's diameter. Sounds easy to replicate in real life right? Well, it's not. Circles are "a shape of Euclidean geometry that is the set of all points in a plane that are a given distance from a given point, the centre." That means that every point on the circle is the same distance from the centre as every other point. If this doesn't hold true, then you haven't got a perfect circle; you've just got something that looks quite like a circle, without actually being one.

Given the limitations of the universe again, it is impossible to construct a perfect circle. If you have two points next to each other, no-matter how small the distance between them, you can always find a point in between. This effectively means that the number of points in a perfect circle tends to infinity. At some point you will either reach the minimum length in the universe, or run out of stuff to construct your circle with. Either way, you have not been able to construct a perfect circle, and thus are not able to calculate the true value of Pi.

This is about as absurd as saying given the limits of the universe, it is impossible to construct a perfect vacuum, therefore speed of light in vacuum is not a property of the physical universe, but a invented number.

Nor is the rest any less absurd than that finding natural occurrences of two related properties in the universe to seem to converge on a irrational dimensionless multiplier, and claiming by its irrationality the relationship itself is thus an invention.