Answer from Dr. Joffre Mercier, Brock University:
Pi is defined, and it has been defined for a very long time!
Pi is the ratio of the circumference to the diameter of a circle. In other words, Pi is calculated by dividing the circumference of a circle (i.e. the distance of the circle's perimeter) to that circle's diameter (the distance across the circle at its widest point). This calculation gives a value of approximately 3.14159, but continuing the calculation gives series of numbers in which the decimals never repeat. I think that the person is asking whether or not we will ever find repeating decimals in Pi. The answer is probably not!
Answer from Dr. Michael Winter, Brock University:
Pi has already defined for more than 2000 years. It is the ratio of a circle's circumference to its diameter. My guess here is that the question actually asks something different, namely, will we ever know all digits of Pi? Here, the answer is no. Pi is an irrational number,
i.e., is not a fraction, so that the decimal representation will never end and will not become periodical.