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- TL;DR Summary
- 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 can't 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 can't 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 can't 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?

and so on. pi is irrational and you can't 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 can't 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 can't 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?