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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"?

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/
```
Associated Topics:
High School Transcendental Numbers
Middle School Pi

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