Simple question really: If pi is an irrational number, what does that say about circles and our measurements?

If we accept that pi is an irrational number and then we continue our discussion that pi is just described/accepted as the ratio of the circumference and diameter of the circle.

My question now poses, that if pi is a result of the ratios then that means either the circumference and diameter or both of a circle are irrational numbers because by the closure of rational numbers under the division operator, we could never obtain an irrational number from the division of two rational numbers but then what does this mean? Can the same argument apply to the real world and real measurements?

Now, imagine a thread and wrap it alongside the edge of a coin so that it takes the shape of a 'circle'(not perfect because perfect circles don't exist) then the wrap-length of that thread will definitely be finite assume another thread for the diameter this will also be a finite length of thread. Now unwrapping, the thread that represents the circumference we see that the length of the thread for the circumference is larger than the thread for the diameter by a certain factor. Can we say that this factor is irrational, but it can't be can it? Can we say that the initial measurements for the lengths of the thread, are represented by rational or irrational numbers?

Does this say something about the nature of the circle, lines and mathematics because if we say that the ratio between the two threads is irrational that means one or both of the lengths of the threads is irrational both these threads are straight lines with endpoints in the geometrical sense. So does that mean every 'conceived' and/or 'real' length is always an irrational number and does that mean that rational numbers are actually the 'irrational' ones, we create for this weird sense of comfort?

To make my question clearer, I have mentioned above that we use a thread and a coin for thinking about the circle but this was much more realistic and so I just want one to think of an abstract circle and then cut that circle and stretch out the line that makes the circle, now I am saying even in the abstract sense that either the line that makes the circle or the line that went through the center of the circle i.e., the diameter is actually irrational, because of closure under division and with the fact that the perimeter of any other shape can be congruent with the circumference of the different sizes of circles this means that every perimeter and every line conceivable must be irrational?

• Pi can be irrational even if the length of any real, physical circle's diameter or circumference is entirely rational. That's because pi can be seen as a limit to the relationship between circumference and diameter of any physical circle, rather than the actual relationship for any given specific physical circle.
– TKoL
Commented Mar 29 at 16:14
• Pi is abstract, not physical - physical stuff isn't perfect.
– TKoL
Commented Mar 29 at 16:15
• There is no actual number that is the correct measurement. There is an error range that contains an infinite number of rational and irrational numbers. Commented Mar 29 at 16:19
• Your question is quite analogous to this. Please see my answer there Commented Mar 29 at 18:06
• @Rushi beautifully and well explained, thank you. Commented Mar 29 at 18:11