As I took the day off sick, through boredom I will post the following challenge just for fun (proper mathematicians are barred for the moment).

Let S be a circle with radius r and circumference C. Then we know that C = 2πr.

We easily see that π= C/2r = C/d

where d = 2r = diameter.

Suppose the C is some integer. Suppose further that d is integer. Then π = C/d, a rational number. Therefore, π is rational!

Whoops, what's wrong?