B measuring a circle and the Uncertainty principle

making exact measurements of a circle.
I have been trying to see if my understanding of uncertainty principle is right. So I thought consider a circle. for this augment we will look at its diameter and it circumference. Suppose you get a length of string and make a exact measure of the circles circumference using this length of sting, we will call this length of string One circumference unit or 1.00 cf. it is exactly one unit. Now if you use the same unit to measure the diameter it would be 1/pi . and that would be 0.31830988618......
and so on. pi is irrational and you cant get an exact figure. if you do the opposite say, use a string to measure the diamiter and call it 1 diamiter legnth or say 1dl. then measure the circumphrence with one dl of string it would be equil to pi or 3.14159265359.... and you cant get an exact measure of it because pi is irational. It seams that with a cicle I can only know the exact length of diameter but not circumfrence or know exact length of circumfrence but not the diameter. So I cant know the exact length of both. Is this an example of the Uncertainty principle? If so, does it prove that Uncertainty principle is a fundamental mathematical principle and not just a result of us not having good enough ruler?
This has nothing to do with the uncertainty principle. The uncertainty principle is an inequality that applies to non-commuting observables.
Summary: making exact measurements of a circle.

Is this an example of the Uncertainty principle?
No. The uncertainty principle places a limit on the precision with which you can know the product of specific pairs of observables. There is no limit to the precision with which you can know ##\pi##


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This topic is full of difficulties. It turned up recently somewhere else on PF. There is actually no problem mixing rational and irrational values of length. It happens all the time because both kinds of number are in the set of Real Numbers. In practical terms, there is no problem either because the accuracy of measurement is very clumsy and any value measured on a 'ruler' includes (many) both rational and irrational values within its error bars.
Engineers shouldn't try messin' with Mathematicians - they will lose.
(I am an Engineer, btw.)

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