Here is a question which has been puzzling me for some time.
You have a thin rope of an integer length $L$. You can bend it to create a rectangle of perimeter $L$. Fine so far.
Next, through some mechanism, you create a circle with the rope. This circle has a perimeter of $L$.
But then $L = 2\pi r$.
This suggests that $L$, which is a multiple of $\pi$, must be irrational too.
What am I missing?