Akhilesh Trivedi wrote:One question Pi was discovered or invented?
Of course it is an invention!
Mathematics itself is an invention. It doesn't exist by itself. Pi was established as part of the mathematics, so it is an invention too.
You might say that Pi exists "physically" - after all, it is in certain sense present in every circle or sphere, and the universe contains lots of spheres (starts and planets, for example). But! These spheres are not perfect, and even if there was a perfect sphere, due to quantum theory limitations no one can measure the circumference and volume precise enough to obtain Pi this way. Further, our space is actually not euclidean, which means that even for a perfect circle the ratio of its circumference to its diameter is not exactly equal to Pi - due to the curved space the perfect circle resides in. (Yes, the sum of angles in a triangle is not 180 degrees. They lied to us in school!)
As has been shown, Pi it is just an abstract, idealized concept, it doesn't physically exist in the universe. Therefore it couldn't be discovered and was necessarily invented.