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Pi must repeat

Name: Anonymous 2008-02-05 12:57

If Pi has infinite numbers following the decimal, at same point those numbers must fit into a sequence that has already been done, for whatever length of numbers.  Mathemetecians need only figure out how many numbers are repeated and for how long and in what places of the sequence.

Name: Anonymous 2008-02-14 21:17

>>58

That is a good question.  Pi is not the root of any "polynomial" equation where the polynomials have powers of x that are fractions, either positive or negative.

For radical exponents, I believe the question is open.  That means we don't know the answer. 

If you allow *arbitrary* exponents, pi is a root of a zillion different equations.   For example, pi is a root of the equation x^q - 2 = 0, where q = log(2)/log(pi). 

If you allow the "polynomials" to have infinitely many terms, you can find equations of which pi is a root.  For example, it is the smallest positive root of
x - x^3 / 6 + x^5 / 120 - x^7 / 5040 + ... .   But this isn't a polynomial.

I hope this does more to clear up the situation than it does to confuse it.

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