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 |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/