Proving Pi is IrrationalDate: 01/06/99 at 19:14:16 From: Blake Sandler Subject: Repeating Pi Dear Dr.Math, How do you know that pi never repeats? I mean, it could be repeating by the billions. Does a computer bleep, "NO PATTERNS"? From, Blake Date: 01/06/99 at 19:41:24 From: Doctor Wilkinson Subject: Re: Repeating Pi An excellent question! You are quite right that no matter how many digits you compute, you cannot be sure that way that the digits might not eventually repeat. But it is possible to prove that pi is not the ratio of two integers (that is, that pi is an irrational number). The proof is quite difficult; a simple version of it, courtesy of Robert Simms, appears in this Dr. Math conversation: Irrationality of Pi httphttp://mathforum.org/library/drmath/view/55828.html - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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