Proving Pi is Irrational

Date: 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). But 
the proof is quite difficult. If you want to see what even a simple 
version of this looks like, see

   http://www.math.clemson.edu/~rsimms/neat/math/pi/piproof.html   

- Doctor Wilkinson, The Math Forum
  http://mathforum.org/dr.math/