We could make an object that is exactly pi meters long. Make a circle of 1 meter in diameter, and then straighten it out. We would not be able to measure the length more accurately than we can calculate it (that might be the largest understatement ever) but to the tolerance with which we could make a 1 meter diameter circle, you should have the same tolerance to the circumference being pi.
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
We could make an object that is exactly pi meters long. Make a circle of 1 meter in diameter, and then straighten it out. We would not be able to measure the length more accurately than we can calculate it (that might be the largest understatement ever) but to the tolerance with which we could make a 1 meter diameter circle, you should have the same tolerance to the circumference being pi.
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.