Silly Question about $π$

Question

In our junior classes, we learnt that $π$ is an irrational number. Now, also we know about rational numbers. So, if I say that I have a thread of 44cm long and we may convert it into a circle. Then how come we can say that our measure for the thread is correct. Also I may, then, assume that every measure is therefore not correct even that precise sample that has been kept as the standard unit 1 metre length scale. So is for the whole universe or any system. Is it correct? Any reviews?

Thanks for seeing this silly question! :)

Answer 1

“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle

So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.

Mathematics is precise.

Answer 2

A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2\pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2\pi$ is an approximation for these rational numbers.

In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.

(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)

Answer 3

I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.