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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"?


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

Irrationality of Pi

- Doctor Wilkinson, The Math Forum
Associated Topics:
High School Transcendental Numbers
Middle School Pi

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