Pi: Exact Number vs. Unending Representation

Date: 09/15/2004 at 21:58:24
From: Amanda
Subject: pi

If pi is a number that doesn't end how is it that pi is an exact 
number on the number line?  If the number doesn't end how can it be an
exact number?

Date: 09/15/2004 at 22:44:16
From: Doctor Luis
Subject: Re: pi

Hi Amanda,

You've hit on a two thousand year old question!

The reason it's still an exact number is that each decimal that keeps
getting added is smaller and smaller.  They get so small, that even
after you add an infinite number of them, they don't grow the number
by that much.  Eventually, you just end up with the excact number pi.

Conceptually, this is related to Zeno's Paradox.  Zeno was a 
philosopher who lived a long time ago in Greece, and didn't believe
that you could add up a bunch of small numbers and end up with 
something that isn't infinite.  Fortunately for us, he was wrong,
or we wouldn't be able to walk anywhere.  What do I mean by this?  You
should probably take a look at our archives, where Doctor Mike takes
on that very question:

  Halving and Halving Again - Zeno's Paradox
   http://mathforum.org/library/drmath/view/52507.html 

I hope this helped!  Let us know if you have other thought-provoking
questions.

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

Date: 09/16/2004 at 19:44:42
From: Amanda
Subject: Thank you (pi)

Dear Doctor Luis,

Thank you very much for answering my question.  I greatly appreciate it.

    Amanda