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Why can't $\pi$ be expressed as a fraction?
If pi is the ratio of a circle's circumference to its diameter, why can't we simply take a circle, measure its circumference and diameter, and derive the fraction?
Say we have a string of some length and we place it such that it forms a circle. Then we will know the circumference and we can measure the diameter. The diameter might be difficult to measure but its length surely is some fixed number. If it's not possible to do this, does it that mean that the limit to determining the exact value of pi is only technological and not mathemetical?