Was pi invented or discovered?

[Tiberius]

Colours don't "exist" per se... the frequency of the light entering our eyes gets interpreted by the brain and in turn we have the experience of colour from a physical phenomena (the frequency of the light) that has a huuuge range, not just the range where colours "exist".

Colors exist due to that interpretation though. We can get all philosophical and say that colors only exist if there is something to view them, which is true enough, but when we are talking about discovery / invention, it's quite obvious to me that colors were discovered rather than invented.

Names of colours, well yes, they were invented, but the colors they actually represent were not.

Another observation that sort of ties in with the above is that the colour "red" isn't an objective thing. In the colour spectrum, where does red begin and end?

True, but that doesn't negate colors existing prior to humans, it only demonstrates a limitation on human descriptions of colors.

Having thought through this a bit more, it really all depends on what you define "discovery" and "invention" as. Pi is a property of perfect circles, which we definitely did invent (they do not make an appearance in the physical world, nor can they). Now, one could say that since Pi was worked out by taking a perfect circle and dividing the circumference by the diameter, it counts as a discovery (or a discovery of an invention). If you want to look at it that way, fine, I have no objection. However, the point is that the "discovery" of Pi was based on an invention of humans, and nothing else. I still think it's easier to think of Pi as having been invented, given that perfect circles were also invented.

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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.

There is a difference between the actual speed of light in a vacuum, and c, which is an estimation of that speed. The actual speed of light is clearly a property of the physical universe; light exists and it moves. The value we have assigned c is an invented number, as accurate as we can currently get it (and it's currently based off a 2009 calculation as far as I can tell). We are trying to get more accurate, but due to the limitations you noted above, as well as computational limitations, it's unlikely we'll ever get the true value (though perhaps we may be able to infer it).

In terms of Pi, the analogy here would be that however hard you try to make a perfect circle in the physical world, if you take the circumference of that circle and divide it by the diameter, you will never end up with the actual value of Pi.

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.

The "related properties" I assume you are talking about here are the circumference and the diameter of a perfect circle? If so, then what you've said is categorically wrong. Those properties do not make any "natural occurrences" in the universe, because it is impossible to find (or construct) a perfect circle in the universe. You can only get the irrational number Pi by creating a perfect circle. Any imperfect circle will get you a number that does not equal Pi (though it may be very close).