[ckissick]

Originally Posted by jyl

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.

Let's say r=10/sqrt(pi)

Then r= 10/1.7724...
r=5.6418...

Then A=pi*5.6418...^2

Or, A=100.0000000...

So, there are an infinite number of circles with an area that is a rational number. And an infinite number of circles with an area that is an irrational number. Whoa, that's weird.