Perhaps the best way to put it is that we are unable to calculate the precise area of a circle because our mathematics are not sufficient to do so.
Actually, I have to agree with stefcep2 here. Our mathematics is fine in this regard. The area of any circle is
pi*r*r. For any given value of r, we can quote the precise area, albeit as a factor of
pi.
The precise value of
pi is the problem. In our preferred number base,
pi, like
e, just isn't a convenient value to work with. There are a number of geometic and algebraic series solutions to calculate
pi. We can calculate it to any arbitrary precision we want, it has been calculated to over 1 billion decimal places by the end of the 1980's.
The problem is, we don't know if
pi is normal or not. It certainly isn't normal up to as many decimal places have been computed. The same is true for
e, nor do we know if they are truly independent.
So, I would suggest stefcep2 is correct to use the term indeterminate.
