My answer to: (Question details: 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 mathematical?) (To vote and comment on Quora, visit the link here.)
Your idea is perfectly fine, i.e. to measure the circumference and the diameter and report the ratio as pi. But the trouble is that you first have to MEASURE the circumference exactly for that! It so happens, my friend, that this bloody circumference always changes when you use a lower least count. It doesn’t get to a value which is same as a previous value, even if you use a least count of a hundredth of a millimetre. Now tell me, how can we measure the two and divide them to get a DEFINITE value of pi?
And that is the reason, that there are people who choose to spend their lives calculating pi to the millionth decimal place instead of just dividing the circumference by diameter after measuring them.
You see, it’s not a rectangle where we can choose the length and breadth as we want. In a circle, the circumference will change when you change the diameter, and so you will have to tolerate the tantrums of pi.