How can Pi be Irrational?

Date: Wed, 1 Nov 1995 15:29:43 -0500
From: Anonymous
Subject: irrationality of pi

A student asked "how can pi be irrational if it is defined as the 
ratio of two rational numbers?"  I have no clue and neither did 
anyone in my department.  What do you think?

Date: 11/2/95 at 15:26:19
From: Doctor Ethan
Subject: Re: irrationality of pi

That is a really interesting question.

The problem is with how you are understanding the numbers in the 
definition of pi.

Pi is defined to be the ratio between the diameter and the 
circumference of a circle.  However, these will never be two 
rational numbers.

When you measure them you are approximating them, and then you can 
take their ratio to find an approximation of pi.

Does that make sense?  It can never be that the diameter and the
circumference will both be rational numbers.  If this bothers you 
then you join the ranks of the great mathematicians who founded 
geometry who also were bothered by the irrationality of Pi.

Hope this helps.

Write back if you have any more questions.

-Doctor Ethan,  The Geometry Forum