Interesting, irrational numbers.
Irrational number - Wikipedia, the free encyclopedia
On the OQ, I believe
most circles have area that is an irrational number. But not all.
You may read that "all" circles have area that is an irrational number, e.g. here is a blogger at
Plato's Heaven: Can't square a circle
who states
"all circles have a circumference and an area which is irrational."
But that seems evidently
false to me. Suppose radius r = sqrt ( X / pi ) where X is any rational number. Then area is X = pi * r^2 and is, almost definitionally, a rational number.
Seems like an example of not believing everything you read on the Internet.
Does anyone see something wrong in my logic?