Do you have any resource that you can point me to that speaks about the relationship of limiting constructions to irrational numbers? (Not being the usual
I guess that I ask the question because there are perfectly boring shapes that give rise to irrational numbers, like a the hypotenuse of a right triangle with two sides of length one.
There are also a lot of rational limits that converge to rational numbers.
I have just never heard of any explicit connection.