As you know, the four-fours classical problem consists in expressing the first integer numbers using algebraic expressions involving only four fours, either alone or concatenated. Operators '+', '-', '*', '/', '^' and functions 'sqrt(x)' and 'x!' (on HP calculators) are allowed.
Thus,
0 = 44 - 44
1 = 44/44
2 = 4/4 + 4/4
3 = (4 + 4 + 4)/4 or sqrt(4 * 4) - 4/4
4 = 4 + (4 - 4)/4 or 4! -(4 * 4) - 4
5 = (4 * 4 + 4)/4 or sqrt(4 * 4) + 4/4
and so on.
The four-fours problem originally applies only to integers. What about expanding it to include an exact representation of pi, while sticking to the rules above?