How do I correctly measure the circumference of a circle

Question

I found How exactly do you measure circumference or diameter? but it was more related to how people measured circumference and diameter in old days.

BUT now we have a formula, but the value of PI cannot not be accurately determined, how can I find the accurately calculate the value of circumference of a circle?

Is there any other may be physical mean by which I can calculate the correct circumference?

thank you

Answer 1

The correct answer to the question what the circumference of a circle with diameter $d$ would be $\pi \cdot d $. Of course this is not a satisyfing answer. But since this ridiculous number $\pi$ cannot even be described by the root of a polynomial with coefficients in $\mathbb Q$ we can only approximate $\pi$. This is not a bad thing though. For most, if not all, applications we can approximate $\pi$ good enough so we don't realize it is an approximation. For pure mathematics, we can just use the symbol ''$\pi$''

I hope this helps you a bit

Answer 2

Construct the circle of diameter 1/pi. The circle has circumference =1. It’s sure exact value. (You don't escape from pi - it's property of each circle).

Answer 3

We can pretend to measure the circumference of a circle by saying circumference = $\pi$ * diameter

Since $\pi$ itself is an approximation, a "measurement" of the circumference will always and forever be just an approximation and NEVER an exact number. It is quite interesting because one can clearly see a circle has bounds unlike a straight line which can be measured but can go on forever but a circle does not.

Quite mind boggling.