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.
As Vihart once put it, maths is about making up rules and seeing what happens. We didn't discover negative numbers, imaginary numbers, etc. We just wondered what would happen if you could subtract larger numbers from smaller numbers, or could multiply two equal numbers together to get a negative number, and created a way to make it work whilst being consistent with other parts of mathematics.
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.
As Vihart once put it, maths is about making up rules and seeing what happens. We didn't discover negative numbers, imaginary numbers, etc. We just wondered what would happen if you could subtract larger numbers from smaller numbers, or could multiply two equal numbers together to get a negative number, and created a way to make it work whilst being consistent with other parts of mathematics.
